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