Question

Please answer this question I need it i. Vertex and standard form.

Answer 1

Equation :

This parabola is facing downwards and highest point of the parabola is it's vertex.

Highest point is (-2,2)

so the vertex is (-2,2)

The graph is passing through (-1,0)

Equation in vertex form is

$y = a(x - h) {}^{2} + k$

$0 = a( - 1 + 2) {}^{2} + 2 \\ 0 =a (1) {}^{2} +2 \\ 0 = a + 2 \\ a = - 2$

Substitute back in Equation

$y = - 2(x + 2) {}^{2} + 2$

the graph has two x intercepts -1 and -3

that means (x+1) and (x+3) are the factors

multiply factors to get the equation in standard form

$-2(x + 1)(x + 3) = 0 \\ -2(x {}^{2} + x + 3x + 3) = 0 \\ -2( x {}^{2} + 4x + 3) = 0$

-2x^2-8x-6=0