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 9

Question 12345 of 5

Question 1 of 5

A park fountain shoots water upward, and its height above the ground after t seconds is modeled by h (t) = - 16 t^{2} + 32 t + 5, where h (t) is in feet. According to the model, what is the maximum height of the water above the ground?

Explanation For a quadratic function in the form h (t) = a t^{2} + b t + c, the maximum value occurs at the vertex because the coefficient of t^{2} is negative. Here, a = - 16 and b = 32, so the time when the water reaches its maximum height is t = - \frac{b}{2 a} = - \frac{32}{2 ( - 16 )} = 1. Then evaluate the height at t = 1 : h (1) = - 16 (1)^{2} + 32 (1) + 5 = - 16 + 32 + 5 = 21. So the maximum height is 21 feet. Concept summary For a downward-opening quadratic model, the maximum value is the y -value of the vertex. Find the vertex time with t = - \frac{b}{2 a}, then substitute back into the function.

Question 2 of 5

If x satisfies the equation x^{2} = 49, what is the value of x + 2 when x is positive?

Explanation Since x^{2} = 49, the solutions are x = 7 and x = - 7 . The question says x is positive, so x = 7 . Then x + 2 = 7 + 2 = 9 . Concept summary When a quadratic equation gives two possible values, use any condition in the problem, such as positive or negative, to choose the correct one before evaluating the expression.

Question 3 of 5

Which expression is equivalent to x^{2} + 8 x + 12 ?

Explanation To factor x^{2} + 8 x + 12, find two numbers that multiply to 12 and add to 8 . Those numbers are 2 and 6, so the expression is equivalent to (x + 2) (x + 6) . Concept summary A quadratic in standard form can be rewritten in factored form by finding two numbers whose product is the constant term and whose sum is the coefficient of x .

Question 4 of 5

The graph of the quadratic function y = (x - 4)^{2} + 1 is shown in the x y -plane. What are the coordinates of its vertex?

Explanation A quadratic written in vertex form, y = (x - h)^{2} + k, has vertex (h, k) . Here, h = 4 and k = 1, so the vertex is (4, 1) . Concept summary In vertex form y = (x - h)^{2} + k, the vertex is (h, k) .

Question 5 of 5

The system below has exactly one solution (x, y) . y = x^{2} y = 4 x What is the value of x if the solution satisfies x \neq = 0 ?

Explanation Since both expressions equal y, set them equal to each other: x^{2} = 4 x . Then solve: x (x - 4) = 0, so x = 0 or x = 4 . Because the solution must satisfy x \neq = 0, the value of x is 4 . Concept summary For a system involving a quadratic and a linear equation, set the two expressions for the same variable equal and solve for the intersection values.

Your results

0of 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.

Download on the App Store Get it on Google Play

More SAT Math practice

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.

Download on the App Store Get it on Google Play

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.

Download on the App Store Get it on Google Play

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. A park fountain shoots water upward, and its height above the ground after t seconds is modeled by h ( t ) = − 16 t 2 + 32 t + 5 , where h ( t ) is in feet. According to the model, what is the maximum height of the water above the ground?

Q2. If x satisfies the equation x 2 = 49 , what is the value of x + 2 when x is positive?

Q3. Which expression is equivalent to x 2 + 8 x + 12 ?

Q4. The graph of the quadratic function y = ( x − 4 ) 2 + 1 is shown in the x y -plane. What are the coordinates of its vertex?

Q5. The system below has exactly one solution ( x , y ) . y = x 2 y = 4 x What is the value of x if the solution satisfies x  = 0 ?