Unit 8 Review - Quadratic Functions

• less than or equal to 12
• greater than or equal to 12
• less than 12
• greater than 12
• greater than 0 and less than 12

Answer explanation

Graph the function on desmos and look for the vertex. Consider these questions as you look at the graph:

What is the y-value of the vertex?

Is the parabola above or below the vertex?

When heading in the opposite direction of the vertex, does the parabola continue on forever in that direction?

Tags

TEKS.MATH.9-12.VII.B.1

A part of a quadratic function is graphed on the grid. What is the domain of the function shown?

All real numbers ​ (a)   and ​ (b)   .

• greater than or equal to -6
• less than or equal to 6
• less than or equal to 4
• greater than or equal to -4
• greater than -6
• less than 6
• greater than 4
• less than -4

Answer explanation

This is asking for the domain, which are the possible x-values.

Look at the picture, how far does the segment make it to the left (what is the furthest x-value it reaches on the left side)?

Now how far does the segment make it to the right (what is the furthest x-value it reaches on the right side)?

Also, remember - if you can reach/equal that number, you should include "equal to" as part of the answer.

Closed dots mean equal to, open dots mean not equal to.

Tags

TEKS.MATH.9-12.II.C.1

• h(x)
• x
• ≥
• ≤
• 1
• 2
• 5

Answer explanation

Remember, the range is the possible y-values. The variable y can also be represented by h(x) in this function.

Look for the y-value of the vertex, after graphing the function in desmos. Is this the highest value in the function or the lowest?

So does that mean you will be greater than or equal to (≥) or less than or equal to (≤) that value?

Tags

TEKS.MATH.9-12.VII.B.1

• f(x) = -3x^2 - 1

• f(x) = 9x^2 - 18x + 11

• f(x) = -3x^2 + 4x + 1
• f(x) = -3x^2 + 6x - 1

Tags

TEKS.MATH.9-12.II.B.1

The graph of quadratic function h is shown on the grid. Which function is best represented by h?

• h(x) = -x^2 - 2x - 3

• h(x) = x^2 + 2x + 3

• h(x) = -x^2 + 2x - 3

• h(x) = x^2 - 2x + 3

Answer explanation

One way to find the correct answer is to graph each of the answer choices on desmos, and see which one matches the given graph.

Tags

TEKS.MATH.9-12.II.C.1

TEKS.MATH.9-12.II.D.1

TEKS.MATH.9-12.VII.B.1

Based on the graph of a quadratic function, how can you tell the following?

• Intersects the x-axis in only one place.

• When there are three real zeros.

• Never intersects the x-axis.

• When there is one real zero.

• Not possible with quadratic functions.

• When there are no real zeros.

• Intersects the x-axis in two places.

• When there are two real zeros.

Answer explanation

The "zero" is also known as the x-intercept (or solution if solving an equation). A quadratic function can have no real zeros/solutions, 1 real zero/solution, or two real zeros/solutions.

A quadratic function can never cross the x-axis in more than two places.

Tags

TEKS.MATH.9-12.VII.B.1

A graph of a quadratic function is shown on the grid. Complete the statement about the quadratic function.

The function has a ​ (a)   value of ​ (b)   .

• maximum
• 4
• minimum
• 0
• 3
• -3
• 1
• 5

Answer explanation

Remember, the maximum value is the highest value of a parabola (the y-value of the vertex if the parabola is opening down).

The minimum value is the lowest value of a parabola (the y-value of the vertex if the parabola is opening up).

Tags

TEKS.MATH.9-12.VII.B.1

The graph of a quadratic function is shown. Identify the key features.

Axis of Symmetry: ​ (a)  

Vertex: ​ (b)  

Minimum Value: ​ (c)   ​

Y-Intercept: ​ (d)  

Zeros: ​ ​ (e)  

• x = -2
• (-2, -1)
• -1
• (0, 3)
• x = -3 and -1
• x = -3
• x = -1
• (-1, -2)
• (3, 0)
• 3

Answer explanation

Tags

TEKS.MATH.9-12.III.A.1

TEKS.MATH.9-12.VII.B.1

• h(x) = (5x - 2)(x + 2)

• h(x) = (5x + 2)(x - 2)

• h(x) = (x + 2)(x - 2)

• h(x) = (x - 5)(x + 2)

Tags

TEKS.MATH.9-12.II.B.1

TEKS.MATH.9-12.VII.C.1

• g(x) = 2f(x + 1) - 4

• g(x) = f(x + 1) - 4

• g(x) = 2f(x - 1) + 4

• g(x) = f(x - 1) + 4

Answer explanation

Tags

TEKS.MATH.9-12.III.B.1