STAAR Spring 2023 Category 4

The graph of quadratic function h is shown.

Which function best represents h?

• h(x) = x² + 2x - 3

• h(x) = x² - 2x - 3

• h(x) = x² + 4x + 3

• h(x) = x² - 4x + 3

Which statement about f(x) = 4x² - 36x + 81 is true?

• The zeros are 3/4 and -27 because f(x) = (4x - 3)(x - 27)

• The zeros are -3/2 and 27/2 because f(x) = (2x+3)(2x+ 27)

• The zeros are ±9/2 because f(x) = (2x - 9)(2x + 9)

• The zeros are 9/2 because f(x) = (2x - 9)²

Which statement about the function n(x) = 5x² - 20x + 12 is true?

• The domain of the function is x ≥ 2

• The range of the function is n(x) ≥ -8

• The domain of the function is x ≥ 0

• The range of the function is n(x) ≤ 12

An experiment examined the relationship between the number of miles a car traveled, y, per gallon of gasoline and the speed of the car, x, in miles per hour. The table displays the data collected.

A quadratic function can be used to model the data in the table. Which value best estimates the miles per gallon when the speed is 65 miles per hour?

• 27.9

• 31.0

• 40.2

• 24.9

The graph of a quadratic function is shown on the grid.

Which statement appears to be true?

• The function has 3 zeros

• The maximum value of the function is 3

• The vertex of the graph of the function is (4, 1)

• The equation of the axis of symmetry of the graph of the function is x = 1

Which quadratic function in vertex form can be represented by the graph that has a vertex at (1, 46) and passes through the point (3, 10)?

• y = 9(x - 3)² + 10

• y = 9(x - 1)² + 46

• y = -9(x - 3)² + 10

• y = -9(x - 1)² + 46

The table represents some points on the graph of quadratic function g.

What is the range of g?

• All real numbers less than or equal to 3/2

• All real numbers less than or equal to 19/4

• All real number greater than or equal to 3/2

• All real numbers greater than or equal to 19/4

The function f(x) = x² was transformed to create the function g(x) = f(x - 3) - 9. What are the coordinates of the vertex of the graph of g?

Moved the correct answer to each box. Not all answers will be used.

(​ (a)   , ​ (b)   )

• 0
• 3
• -3
• 9
• -9

Function k is defined as k(x) = x² +32x + 248. What are the solutions to k(x) = 0?

• x = -16 + 2√2 and x = -16 - 2√2

• x = 16 + 2√2 and x = 16 - 2√2

• x = -32+ 4√2 and x = -32 - 3√2

• x = 32+ 4√2 and x = 32 - 3√2

The graph of a quadratic function is shown.

Which values best represent the zeros of the function?

Select TWO correct answers.

• x = 1

• x = -4

• x = -1

• x = 3

• x = -3