Question

Write the equation of the quadratic equation function i standard form represented by the graph

Answer 1

`x^(2) +6x+8=0`

Explanation:

we know that

The quadratic equation in standard form is equal to

`ax^(2) +bx+c=0`

In this problem we have

the vertex is equal to the point
`(-3,-1)`

The zeros of the function are the points
`(-4,0)` and
`(-2,0)`

The graph of the figure is a vertical parabola open upward

the equation of a vertical parabola in vertex form is equal to

`y=a(x-h)^(2)+k`

where (h,k) is the vertex of the parabola

substitute

`y=a(x+3)^(2)-1`

with the point
`(-2,0)` find the value of a

`0=a(-2+3)^(2)-1`

`0=a(1)^(2)-1`

`a=1`

the equation in vertex form is equal to

`y=(x+3)^(2)-1`

Convert to standard form

`y=x^(2) +6x+9-1`

equate to zero

`x^(2) +6x+9-1=0`

`x^(2) +6x+8=0`