Question

Find the equation of the quadratic function whose graph is shown below. Given two points. Vertex= (-5,-5) Passes Through (-7,3)

Answer 1

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:

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

• a = vertical stretch
• h = horizontal translation
• k = vertical translation
• (h,k) is the vertex

Plug in the vertex:

`y=a(x-h)^2+k\\y=a(x+5)^2-5`

Plug in the given point and solve for a:

`3=a(-7+5)^2-5\\3=a(-2)^2-53=4a-5\\8=4a\\a=2`

Plug 2 into the equation as a:

`y=2(x+5)^2-5`

Answer

`y=2(x+5)^2-5`