Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 3

Question 1

What is the y-intercept of the quadratic y = 3x² − 4x + 7?

Accepted Answer

7

Answer

The y-intercept occurs at x = 0, giving y = 3(0)² − 4(0) + 7 = 7.

Question 2

Which expression is equivalent to (x + 5)²?

Accepted Answer

x² + 10x + 25

Answer

(x + 5)² = x² + 2(5)x + 25 = x² + 10x + 25.

Question 3

How many real solutions does x² + 4 = 0 have?

Accepted Answer

None

Answer

x² = −4 has no real solutions because no real number squared equals a negative.

Question 4

What is the sum of the polynomials (3x² + 2x) and (x² − 5x + 4)?

Accepted Answer

4x² − 3x + 4

Answer

Combine like terms: (3+1)x² + (2−5)x + 4 = 4x² − 3x + 4.

Question 5

A ball is thrown upward and its height is h = −16t² + 64t. At what time does it reach maximum height?

Accepted Answer

t = 2 seconds

Answer

Using t = −b/(2a) = −64/(2·(−16)) = −64/−32 = 2 seconds.

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