Question

The graphs of f(x) and g(x) are shown below: graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals negative 2.5 times x minus 2 What are the solutions to the equation f(x) = g(x)? x = −3, 4 x = −4, 2.5 x = −0.8, 2.5 x = 8, −8

Answer 1

Answer:

x = −4, 2.5

Step-by-step explanation:

Let's write this problem algebraically

f(x) = x^2 - x - 12

g(x) = -2.5x - 2

We want to find the solutions to the equation f(x)=g(x) so we set them equal to each other

f(x)=g(x)

x^2 - x - 12 = -2.5x - 2

Adding 2.5x and 2 to both sides,

x^2 + 1.5x - 10 = 0

Factoring, we get

(x + 4) (x - 2.5) = 0

So,

x + 4 = 0 ⇒ x = -4

x - 2.5 = 0 ⇒ x = 2.5