Quadratic Functions: Graphing and Equations - College Algebra for Nursing

Question 1

Identify the value of 'a' that will make the parabola ( y = ax^2 + 2x - 1 ) open upward.

Accepted Answer

a > 0

Answer

a < 0

Answer

a = 0

Answer

a = 1

Question 2

The graph of a quadratic function opens downward if its:

Accepted Answer

Leading coefficient is negative.

Answer

Leading coefficient is positive.

Answer

Axis of symmetry is vertical.

Answer

Vertex is a maximum point.

Question 3

Determine the axis of symmetry of the parabola defined by the function f(x) = 2(x - 1)^2 + 3.

Accepted Answer

x = 1

Answer

x = -1

Answer

y = 3

Answer

y = -1

Question 4

Determine the discriminant of the quadratic equation 3x^2 - 5x + 2 = 0.

Accepted Answer

13

Answer

1

Answer

-1

Answer

-13

Question 5

Which of the following is not a characteristic of a parabola?

Accepted Answer

Always increasing or always decreasing

Answer

Having a vertex

Answer

Having an axis of symmetry

Answer

Being a U-shaped graph

Question 6

Find the discriminant of the quadratic function y = x² - 4x + 3.

Accepted Answer

7

Answer

-7

Answer

11

Answer

-11

Question 7

Which of the following is the discriminant of the quadratic equation 3x^2 - 5x + 2 = 0?

Accepted Answer

25

Answer

Cannot be determined

Answer

5

Answer

-25

Question 8

Which of the following is the range of the quadratic function **h(x) = -x² + 4x - 3**?

Accepted Answer

[-3, ∞)

Answer

(-∞, -3]

Answer

[0, ∞)

Answer

(-∞, ∞)

Question 9

What is the minimum value of the quadratic function y = x^2 - 6x + 9?

Accepted Answer

9

Answer

-9

Answer

6

Answer

0

Question 10

What is the shape of the graph of the quadratic function f(x) = x² - 4?

Accepted Answer

A parabola opening upwards

Answer

A straight line with a negative slope

Answer

A parabola opening downwards

Answer

A straight line with a positive slope

Question 11

What are the coordinates of the vertex of the parabola represented by the equation f(x) = 2(x + 3)² - 5?

Accepted Answer

(-3, -5)

Answer

(-3, 5)

Answer

(3, -5)

Answer

(3, 5)

Question 12

What is the discriminant of the quadratic equation x² + 6x + 8 = 0?

Accepted Answer

4

Answer

-4

Answer

20

Answer

-20

Question 13

Which inequality represents the solution set of the quadratic inequality x² - 4 < 0?

Accepted Answer

-2 < x < 2

Answer

x < 2 or x > -2

Answer

x > 2 or x < -2

Answer

-2 ≤ x ≤ 2

Question 14

What is the maximum value of the quadratic function f(x) = -x² + 4x + 1?

Accepted Answer

5

Answer

-5

Answer

1

Question 15

Which of the following equations represents a parabola that opens downward?

Accepted Answer

y = -2x² + 3x - 1

Answer

y = 2x² + 3x - 1

Answer

y = -x² - 3x + 1

Answer

y = x² + 3x - 1

Question 16

Which of the following is a quadratic function?

Accepted Answer

f(x) = 2x² - 5x + 1

Answer

f(x) = x³ - 2x² + 1

Answer

f(x) = 1/x

Answer

f(x) = 3x + 2

Question 17

What is the y-intercept of the parabola represented by the equation y = 2x² - 4x + 5?

Accepted Answer

(0, 5)

Answer

(0, 2)

Answer

(0, -4)

Answer

(0, -5)

Question 18

What is the axis of symmetry for the parabola y = x² + 4x - 5?

Accepted Answer

x = -2

Answer

y = -2

Answer

y = 2

Answer

x = 2

Question 19

Which of the following is the y-intercept of the parabola? y = -x² + 6x - 8

Accepted Answer

(0, -8)

Answer

(0, 1)

Answer

(0, -1)

Question 20

What is the factored form of the quadratic equation  *y = x² - 5x + 6*?

Accepted Answer

y = (x - 2)(x - 3)

Answer

y = (x + 2)(x + 3)

Answer

y = (x - 2)(x + 3)

Answer

y = (x + 2)(x - 3)

Question 21

Which of the following is the standard form of the quadratic equation *y = 2(x - 1)² + 5*?

Accepted Answer

y = 2x² - 4x + 7

Answer

y = -2x² - 4x + 7

Answer

y = -2x² + 4x + 7

Answer

y = 2x² + 4x + 7

Question 22

What is the vertex of the parabola represented by the quadratic function *f(x) = x² - 4x + 3*?

Accepted Answer

(2, -1)

Answer

(4, -3)

Answer

(1, 0)

Answer

(-1, 2)

Question 23

What is the equation of the axis of symmetry for the quadratic function *f(x) = -x² + 5x - 6*?

Accepted Answer

x = 5/2

Answer

x = -5/2

Answer

y = -5/2

Answer

y = 5/2

Question 24

Which of the following describes the graph of the quadratic function *f(x) = (x + 2)² - 3*?

Accepted Answer

A parabola opening upwards with vertex at (-2, -3)

Answer

A hyperbola with vertices at (2, 0) and (-2, 0)

Answer

An ellipse with center at (0, 0) and semi-major axis of 2

Answer

A parabola opening downwards with vertex at (2, 3)

Question 25

What is the sum of the roots of the quadratic equation *x² - 5x + 6 = 0*?

Accepted Answer

5

Answer

2

Answer

-5

Answer

-2

Question 26

What is the product of the roots of the quadratic equation *x² - 5x + 6 = 0*?

Accepted Answer

6

Answer

-6

Answer

-2

Answer

2

Question 27

Which of the following equations represents a quadratic function with a negative leading coefficient?

Accepted Answer

f(x) = -x² + 3x - 2

Answer

f(x) = 2x² - 3x - 2

Answer

f(x) = -2x² + 3x + 2

Answer

f(x) = x² + 3x - 2

Question 28

Which of the following is the graph of a quadratic function?

Accepted Answer

A parabola

Answer

A hyperbola

Answer

A circle

Question 29

What is the vertex of the parabola represented by the equation *y = x² - 4x + 3*?

Accepted Answer

(2, -1)

Answer

(-1, 2)

Answer

(1, -2)

Answer

(0, 3)

Question 30

What is the axis of symmetry of the parabola given by the equation: y = -2x^2 + 4x - 1?

Accepted Answer

x = 1

Answer

y = 1

Answer

x = -1

Answer

y = -1

Question 31

What is the discriminant of the quadratic equation: 2x^2 - 5x + 3 = 0?

Accepted Answer

-7

Answer

-3

Answer

7

Question 32

Which of the following is the equation of the quadratic function whose graph has a vertex at (-2, 1) and passes through the point (1, 4)?

Accepted Answer

y = x^2 + 4x + 1

Answer

y = -x^2 - 4x + 1

Answer

y = -x^2 + 4x + 1

Answer

y = x^2 - 4x + 1

Question 33

What is the y-intercept of the parabola given by the equation: y = -x^2 + 2x - 3?

Accepted Answer

-3

Answer

1

Answer

3

Answer

-1

Question 34

Which of the following is the range of the quadratic function: y = x^2 - 2x?

Accepted Answer

[0, ∞)

Answer

[0, 1]

Answer

-∞, ∞

Answer

(-∞, 0]

Question 35

What is the domain of the quadratic function: y = 1/(x^2 - 1)?

Accepted Answer

All real numbers except x = ±1

Answer

All real numbers

Answer

x < -1 or x > 1

Question 36

Which of the following is the equation of the quadratic function that has x-intercepts at (2, 0) and (-3, 0)?

Accepted Answer

y = x^2 - 5x + 6

Answer

y = -x^2 - 5x + 6

Answer

y = -x^2 + 5x + 6

Answer

y = x^2 + 5x + 6

Question 37

What is the maximum value of the quadratic function: y = -x^2 + 4x + 1?

Accepted Answer

5

Answer

1

Answer

-5

Question 38

Which of the following equations represents a quadratic function?

Accepted Answer

y = x^2 - 3x + 2

Answer

y = 1/x

Answer

y = x^3 + 2x

Answer

y = 2x

Question 39

What is the vertex of the parabola represented by the equation y = (x - 3)^2 + 1?

Accepted Answer

(3, 1)

Answer

(3, -1)

Answer

(1, 3)

Question 40

What is the axis of symmetry of the parabola represented by the equation y = -2x^2 + 4x + 3?

Accepted Answer

x = 1

Answer

y = -1

Answer

y = 1

Answer

x = -1

Question 41

Which of the following is the y-intercept of the parabola represented by the equation y = x^2 + 2x - 5?

Accepted Answer

-5

Answer

5

Answer

1

Answer

-1

Question 42

What is the discriminant of the quadratic equation 2x^2 - 5x + 3 = 0?

Accepted Answer

1

Answer

9

Answer

-9

Answer

-1

Question 43

Which of the following is a true statement about the graph of the parabola represented by the equation y = -x^2 + 4x - 3?

Accepted Answer

Opens downward and has a maximum value of 1

Answer

Opens upward and has a maximum value of 1

Answer

Opens downward and has a minimum value of -3

Question 44

What is the equation of the parabola that has a vertex at (2, -1) and passes through the point (1, 0)?

Accepted Answer

y = (x - 2)^2 - 1

Answer

y = (x + 2)^2 - 1

Answer

y = (x - 2)^2 + 1

Answer

y = (x + 2)^2 + 1

Question 45

Which of the following transformations would shift the graph of the parabola represented by the equation y = x^2 to the left by 2 units?

Accepted Answer

y = (x + 2)^2

Answer

y = x^2 + 2

Answer

y = (x - 2)^2

Answer

y = x^2 - 2

Question 46

What is the vertex form of the quadratic equation 4x^2 - 12x + 9 = 0?

Accepted Answer

y = (x - 3)^2

Answer

y = (x + 3)^2

Answer

y = 4(x - 3)^2

Answer

y = 4(x + 3)^2

Question 47

Which of the following is a characteristic of the graph of a quadratic function?

Accepted Answer

It is a U-shaped curve

Answer

It is a straight line

Answer

It is a hyperbola

Answer

It is a circle

Question 48

Which of the following is the equation of a parabola with a vertex at (2, -3) and a focus at (2, 0)?

Accepted Answer

y = 1/12(x - 2)^2 - 3

Answer

y = 1/4(x - 2)^2 - 3

Answer

y = -1/4(x - 2)^2 - 3

Answer

y = -1/12(x - 2)^2 - 3

Question 49

What is the axis of symmetry of the parabola y = (x + 3)^2 - 2?

Accepted Answer

x = -3

Answer

x = 3

Answer

y = 2

Answer

y = -2

Question 50

Which of the following is the discriminant of the quadratic equation x^2 - 5x + 6 = 0?

Accepted Answer

-11

Answer

1

Answer

11

Answer

-25

Question 51

What is the range of the parabola y = -x^2 + 4x - 3?

Accepted Answer

[-3, -∞)

Answer

(-∞, -3]

Answer

(∞, 3]

Answer

[3, ∞)

Question 52

Which of the following is the equation of the quadratic function that passes through the points (-1, 2), (1, 0), and (2, -2)?

Accepted Answer

y = -x^2 + x + 2

Answer

y = x^2 - x + 2

Answer

y = x^2 + x + 2

Answer

y = -x^2 - x + 2

Question 53

What is the vertex form of the quadratic equation y = x^2 - 6x + 8?

Accepted Answer

y = (x - 3)^2 - 1

Answer

y = (x + 3)^2 - 1

Answer

y = (x - 3)^2 + 1

Answer

y = (x + 3)^2 + 1

Question 54

Which of the following is the solution to the quadratic inequality x^2 - 4x + 3 > 0?

Accepted Answer

x < 1 or x > 3

Answer

x < 3 or x > 1

Answer

x > 1 and x < 3

Answer

1 < x < 3

Question 55

What is the domain of the quadratic function f(x) = sqrt(x - 2)?

Accepted Answer

[2, ∞)

Answer

(2, ∞]

Answer

(0, 2]

Answer

[0, 2]

Question 56

Which of the following is the inverse of the quadratic function f(x) = 2x^2 + 1?

Accepted Answer

f^-1(x) = ±√((x - 1)/2)

Answer

f^-1(x) = (x - 1)/2

Answer

f^-1(x) = (x + 1)/2

Answer

f^-1(x) = 2√(x - 1)

Question 57

What is the area of a rectangle with a length of (x + 2) units and a width of (x - 1) units?

Accepted Answer

x^2 + x - 2

Answer

2x^2 - x - 2

Answer

2x^2 + x - 2

Answer

x^2 - x - 2