Solving and Factoring Quadratic Expressions and Equations

When checking to see if a quadratic trinomial is a Perfect Square Trinomial, you must determine if the first and last terms are perfect squares and if the middle term is the product of 2 times the square roots of the first and last term. The first and last terms must also be positive.

• True

• False

What are some similarities and differences between Perfect Square Trinomials and the Difference of two squares?

Evaluate responses using AI:

OFF

(x + 2)(x - 3) = 0

• x = -2 and 3

• x = 2 and 3

• x = -2 and -3

• x = 2 and -3

Factor
k²+7k+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

What is the first step in solving

(x + 2)(x - 3) = 0 ?

• Plug in zero for x

• Combine like terms

• FOIL

• Set each binomial factor equal to zero

Factor: x² - x -12

• (x - 4)(x + 3)

• x = 4 and -3

• (x - 3) (x + 4)

• x = 3 and -4

(x + 4)(x + 7) = 0

• x = 4 and 7

• x = -4 and 7

• x = 4 and -7

• x = -4 and -7

Which equation is the standard form of a quadratic function?

• f(x) = mx + b

• f(x) = a(x - m)(x - n)

• f(x) = ax² + bx + c

• f(x) = a(x - h)² + k

What is a quadratic function in factored (intercept) form with x-intercepts of 5 and -2

• f(x) = x² + 3x -10

• f(x) = (x + 5)(x - 2)

• f(x) = (x - 5)(x + 2)

• f(x) = (x + 1.5)² - 12.25

The rule we can use to help us solve for the x-intercepts of a quadratic is called the ________ product property.