Question

I need help with this please

Answer 1

Answer:

$y = x^2 + 6x + 8$

Step-by-step explanation:

The equation can be written using information from the graph. The vertex of the parabola is (-3,-1). Use the vertex form $y = a(x-h)^2 + k$ by substituting h = -3 and k = -1. The equation becomes $y = a(x--3)^2 + -1$. It simplifies to $y = a(x+3)^2 - 1$. To find a, substitute the point (x,y) on the graph into the equation and solve for a. Substitute x = -2 and y = 0.

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

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

$0 = a - 1$

$1 = a$

So the equation is $y = (x+ 3)^2 - 1$. Convert to standard form by distributing the parenthesis and combining like terms.

$y = (x+ 3)^2 - 1\\y = x^2 + 3x + 3x + 9 - 1\\y = x^2 + 6x + 8$