write an equation for a quadratic function with a graph that has its vertex ay (-5,7)

Question

write an equation for a quadratic function with a graph that has its vertex ay (-5,7)

Answer 1

The vertex form of a quadratic function looks like the following:

          y = a(x - h)² + k ,  where (h, k) is the vertex of the graph of the function.

Given the graph of a quadratic function whose vertex is at (-5, 7), where -5 = h and 7 = k, we can write an equation for the quadratic function in vertex form:

          y = a(x - h)² + k      ,          (h, k) = (-5, 7)

          y = a(x - (-5))² + 7

          y = a(x + 5)² + 7          ==>    where  a = 1

          y = (x + 5)² + 7

Now we can convert this into the standard form of a quadratic equation, which looks like the following:

          y = ax² + bx + c   

     y = (x + 5)² + 7 

     y = (x + 5)(x + 5) + 7

     y = (x² + 5x + 5x + 25) + 7

     y = x² + 10x + 32               ==>     where  a = 1,  b = 10,  c = 32

Answer 2

Hello, Oksana ---

You can designate the form of the quadratic from the vertex, (h, k).

A parabola with vertex (h, k) would have this form:

    y - k  =  a(x - h)² 

Substituting your numbers, you would have:

     y - 7  =  (x + 5)²

It could have an infinite number of variations, depending on whether there was a real number "a"  (not 0) in front of the (x-h)² term. 

If you use a = 1, multiply it out and put it into y = form, you would have:

     y = x² + 10x + 32

Answer 3

An hyperbola with one of its apices at (-5,7) is one way to satisfy this.  Make it easy on yourself and use an upright parabola.

y - 7 = (x - (-5))^2,   

y  -  7 = (x  +  5)^2