Keystone Test Keystone Algebra: Polynomials and Quadratic Functions

Question 1

What is the standard form of a quadratic equation?

Accepted Answer

ax² + bx + c = 0

Answer

The standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0.

Question 2

Which of the following is a polynomial expression?

Accepted Answer

3x² + 2x − 5

Answer

A polynomial has non-negative integer exponents, so 3x² + 2x − 5 qualifies.

Question 3

What are the zeros of f(x) = x² − 9?

Accepted Answer

x = 3 and x = −3

Answer

Setting x² − 9 = 0 gives x² = 9, so x = ±3.

Question 4

What is the vertex of the parabola y = (x − 2)² + 5?

Accepted Answer

(2, 5)

Answer

In vertex form y = (x − h)² + k, the vertex is (h, k), so here it is (2, 5).

Question 5

What is the product of (x + 3)(x − 4)?

Accepted Answer

x² − x − 12

Answer

Using FOIL: x·x + x·(−4) + 3·x + 3·(−4) = x² − 4x + 3x − 12 = x² − x − 12.

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