Question

Use the function f(x) = -3x^2+13x+3 to find x when f(x) = -7

Answer 1

x = 5 or x = -
`(2)/(3)`

Explanation:

given f(x) = - 7, then

- 3x² + 13x + 3 = - 7 ( add 7 to both sides )

- 3x² + 13x + 10 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term

product = - 3 × 10 = - 30 and sum = + 13

The factors are + 15 and - 2

Use these factors to split the middle term

- 3x² + 15x - 2x + 10 = 0 ( factor by grouping the 1/2 and 3/4 terms )

- 3x(x - 5 ) - 2(x - 5 ) = 0 ( factor out (x - 5 ) )

(x - 5)(- 3x - 2) = 0

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

- 3x - 2 = 0 ⇒ - 3x = 2 ⇒ x = -
`(2)/(3)`

Answer 2

Answer: - 235

Explanation:

f(x) = -3x² + 13x + 3

f(-7) = -3(-7)² + 13(-7) + 3

= -3(49) - 91 + 3

= -147 - 88

= -235