QuestionFind the intersection points of the quadratics $f(x) = x^{2}+2x-8$ and $g(x) = x^{2}-2x-4$ .

Studdy Solution

STEP 1

Assumptions1. The functions are $f(x) = x^{}+x-8$ and $g(x) = x^{}-x-4$ . The intersection points of the two functions are the x-values where $f(x) = g(x)$

STEP 2

To find the intersection points, we need to set the two functions equal to each other and solve for $x$ .
$f(x) = g(x)$

STEP 3

Substitute the given functions into the equation from2.
$x^{2}+2x-8 = x^{2}-2x-$

STEP 4

implify the equation by subtracting $x^{2}$ from both sides.
$2x-8 = -2x-4$

STEP 5

Add $2x$ to both sides of the equation to isolate the $x$ terms on one side.
$4x-8 = -4$

STEP 6

Add $8$ to both sides of the equation to isolate the $x$ term.
$4x =4$

STEP 7

Divide both sides of the equation by $4$ to solve for $x$ .
$x =1$ The intersection point of the two quadratic functions $f(x) = x^{2}+2x-$ and $g(x) = x^{2}-2x-4$ is $x =1$ .
To find the corresponding $y$ -value, we substitute $x =1$ into either of the original functions. Here, we'll use $f(x)$ .

STEP 8

Substitute $x =1$ into $f(x)$ .
$f(1) = (1)^{2}+2(1)-8$

STEP 9

implify to find the $y$ -value.
$f() = +2 -8 = -5$ So, the intersection point of the two functions is $(, -5)$ .

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