$8x+2=x+4x-6\\\\8x+2=(x+4x)-6\\\\8x+2=5x-6\qquad\text{subtract 2 from both sides}\\\\8x=5x-8\qquad\text{subtract 5x from both sides}\\\\3x=-8\qquad\text{divide both sides by 3}\\\\\boxed{x=-\dfrac{8}{3}}$

5 0

3 years ago

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Find the vertex of the quadratic function f(x) = (x-4) (x+2)

faltersainse [42]

Answer:

vertex = (1, - 9 )

Step-by-step explanation:

The x- coordinate of the vertex is at the midpoint of the zeros.

Given

f(x) = (x - 4)(x + 2)

Find the zeros by letting f(x) = 0 , that is

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 4 = 0 ⇒ x = 4

Then

$x_{vertex}$ = $\frac{-2+4}{2}$ = $\frac{2}{2}$ = 1

Substitute x = 1 into f(x) for corresponding y- coordinate

f(1) = (1 - 4)(1 + 2) = (- 3)(3) = - 9

Vertex = (1, - 9 )

4 0

2 years ago