Math Flashcards

What are the solutions to x² − 7x + 12 = 0?

Answer: x = 3 and x = 4

Factoring gives (x − 3)(x − 4) = 0, so x = 3 or x = 4.

The expression x² + 6x + 9 can be written as (x + a)². What is a?

Answer: 3

x² + 6x + 9 is a perfect square trinomial equal to (x + 3)².

If g(x) = 2x + 1 and h(x) = x² − 3, what is g(h(2))?

Answer: 3

h(2) = 4 − 3 = 1, then g(1) = 2(1) + 1 = 3.

Which expression is equivalent to (3x² − 2x + 5) − (x² + 4x − 3)?

Answer: 2x² − 6x + 8

Distributing the minus sign and combining like terms: 3x² − x² = 2x², −2x − 4x = −6x, 5 + 3 = 8.

What is the simplified value of √48 ÷ √3?

Answer: 4

√48 ÷ √3 = √(48/3) = √16 = 4.

If x² = 25, which statement is true?

Answer: x = 5 or x = −5

Both x = 5 and x = −5 satisfy x² = 25 since squaring removes the sign.

A ball's height is given by h(t) = −16t² + 64t + 5. What is the maximum height in feet?

Answer: 69

The vertex occurs at t = −64/(2 × −16) = 2 s; h(2) = −64 + 128 + 5 = 69 feet.