SAT Quadratic Equations And Functions Practice Questions (Free + Explanations)

Advanced Math · Quadratic Equations And Functions

SAT Quadratic Equations And Functions Practice Questions (Free + Explanations) | Quiz 10

Question 12345 of 5

Question 1 of 5

The table shows values of a quadratic function f . x f (x) - 2 8 - 1 3 00 1 - 1 20 Based on the table, what is the value of f (3) ?

Explanation From the table, f (0) = 0 and f (2) = 0, so the quadratic has zeros at x = 0 and x = 2 . That means it can be written as f (x) = a (x) (x - 2) . Using f (1) = - 1, we get - a = - 1, so a = 1 . Thus f (x) = x (x - 2) = x^{2} - 2 x, and f (3) = 3 (3 - 2) = 3 . Concept summary For a quadratic, table values can reveal zeros and help build the factored form, which can then be used to evaluate another function value.

Question 2 of 5

The function f is defined by f (x) = (x - 4)^{2} . Which statement must be true?

Explanation Substitute x = 4 into the function: f (4) = (4 - 4)^{2} = 0^{2} = 0. So the statement that must be true is f (4) = 0 . Concept summary A quadratic written as a square, such as (x - h)^{2}, has a minimum value of 0 when x = h .

Question 3 of 5

The area of a rectangle is given by x^{2} - 16 square units, and its length is x + 4 units. What is the width of the rectangle, in units?

Explanation For a rectangle, area = (length) (width) . So the width is \frac{x ^{2} - 16}{x + 4} . Factor the numerator: x^{2} - 16 = (x + 4) (x - 4) . Then \frac{( x + 4 ) ( x - 4 )}{x + 4} = x - 4. So the width is x - 4 units. Concept summary To find a missing dimension of a rectangle, divide the area by the known dimension. If the area expression is quadratic, factoring can make the division simple.

Question 4 of 5

A company models the height, in feet, of a ball thrown upward from a platform by the function h (t) = - 16 t^{2} + 48 t + 64, where t is the time in seconds after the ball is thrown. According to the model, what is the height of the platform?

Explanation The platform height is the ball's height at the moment it is thrown, so use t = 0 . Substituting gives h (0) = - 16 (0)^{2} + 48 (0) + 64 = 64 . Therefore, the height of the platform is 64 feet. Concept summary In a quadratic model written as h (t) = a t^{2} + b t + c, the constant term c is the initial value, found by computing h (0) .

Question 5 of 5

The graph of the quadratic function y = f (x) crosses the x -axis at x = - 2 and x = 5 . Which equation could define f (x) ?

Explanation An x -intercept at x = - 2 means f (- 2) = 0, so one factor is (x + 2) . An x -intercept at x = 5 means f (5) = 0, so the other factor is (x - 5) . Therefore, a possible equation is f (x) = (x + 2) (x - 5) . Concept summary For a quadratic written in factored form, each x -intercept comes from setting a factor equal to 0 . A zero at x = r corresponds to a factor of (x - r) .

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

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More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. The table shows values of a quadratic function f . x f ( x )  − 2 8  − 1 3  0 0  1 − 1  2 0   Based on the table, what is the value of f ( 3 ) ?

Q2. The function f is defined by f ( x ) = ( x − 4 ) 2 . Which statement must be true?

Q3. The area of a rectangle is given by x 2 − 16 square units, and its length is x + 4 units. What is the width of the rectangle, in units?

Q4. A company models the height, in feet, of a ball thrown upward from a platform by the function h ( t ) = − 16 t 2 + 48 t + 64 , where t is the time in seconds after the ball is thrown. According to the model, what is the height of the platform?

Q5. The graph of the quadratic function y = f ( x ) crosses the x -axis at x = − 2 and x = 5 . Which equation could define f ( x ) ?