Answer: [tex]y=-\dfrac{16}{9}(x+3)^2+4[/tex]
Step-by-step explanation:
Use the vertex formula: y = a(x - h)² + k where
- a is the vertical stretch
- -a is a reflection over the x-axis
- (h, k) is the vertex
We can see that the vertex of the curve is (-3, 4) --> h = -3, k = 4
and it is a reflection over the x-axis --> a-value is negative
We need to find the a-value. Choose another point on the curve and plug it into the vertex formula for (x, y) and then solve for a.
I will choose (x, y) = (-3/2, 0)
[tex]0=a\bigg(\dfrac{-3}{2}+3\bigg)^2+4\\\\\\-4=a\bigg(\dfrac{3}{2}\bigg)^2\\\\\\-4\bigg(\dfrac{2}{3}\bigg)^2=a\\\\\\-\dfrac{16}{9}=a[/tex]
Now that we know the vertex and the a-value, we can input them into the vertex formula:
[tex]\large\boxed{y=-\dfrac{16}{9}(x+3)^2+4}[/tex]
