Key Ideas:
- Finding a quadratic equation
Solving the Question
We're given:
- Vertex= (-5,-5)
- Passes Through (-7,3)
One of the forms of a quadratic equation is vertex form:
[tex]y=a(x-h)^2+k[/tex]
- a = vertical stretch
- h = horizontal translation
- k = vertical translation
- (h,k) is the vertex
Plug in the vertex:
[tex]y=a(x-h)^2+k\\y=a(x+5)^2-5[/tex]
Plug in the given point and solve for a:
[tex]3=a(-7+5)^2-5\\3=a(-2)^2-53=4a-5\\8=4a\\a=2[/tex]
Plug 2 into the equation as a:
[tex]y=2(x+5)^2-5[/tex]
Answer
[tex]y=2(x+5)^2-5[/tex]
