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

-4 , 2.5

Explanation:

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Answer 2

Let's convert the word descriptions into mathematical equations first for illustration.

f(x) = x^2 - x - 12
g(x) = -2.5x - 2

Then, we equate g(x) and f(x). The final equation becomes
x^2 - x - 12 = -2.5x - 2

Then, we simplify by transposing and combining like terms.
x^2 - x + 2.5x -12 + 2 = 0
x^2 + 1.5x - 10 = 0

Since this is a quadratic equation, we find the roots by using the quadratic formula


`x=[-b \ +/- \sqrt{ b^(2) -4ac}]/2a`
where a = 1, b = 1.5 and c=-10


`x=[-1.5 \ + \sqrt{ 1.5^(2) -4(1)(-10)} ]/2(1)=2.5`


`x=[-1.5 \ - \sqrt{ 1.5^(2) -4(1)(-10)} ]/2(1)=-4`


Thus, the answer is x = 2.5, -4.