Answer:
[tex]y = -2x^2-4x + 5[/tex]
Step-by-step explanation:
Hello!
We can utilize the vertex form of a parabola to find the equation.
Vertex Form: [tex]y = a(x - h)^2 + k[/tex]
Vertex: [tex](h,k)[/tex]
Vertex
The vertex is the highest or the lowest point of the graph. The vertex of this graph is (-1,7). We can plug that into the formula.
- [tex]y = a(x + 1)^2+7[/tex]
The only missing value now is the [tex]a[/tex] value. We can solve for that by plugging in a x and y value from a point on the graph. I'm going to choose
(0,5).
Solve for a
- [tex]y = a(x + 1)^2+7[/tex]
- [tex]5 = a(0 + 1)^2+7[/tex]
- [tex]-2 = 1a[/tex]
- [tex]-2 = a[/tex]
Plug in the values to get the equation in Vertex Form.
Equation: [tex]y = -2(x + 1)^2 + 7[/tex]
The question is asking for the expanded version of this, so we can multiply it out to find the Standard Form of the parabola.
Expand:
- [tex]y = -2(x + 1)^2 + 7[/tex]
- [tex]y = -2(x^2 + 2x + 1) + 7[/tex]
- [tex]y = -2x^2 - 4x - 2 + 7[/tex]
- [tex]y = -2x^2-4x + 5[/tex]
The Equation is [tex]y = -2x^2-4x + 5[/tex]
