Question

Write a quadratic equation whose graph will have the given vertex.

a. (1.9, −4)
b. (0, 100)
c. (−2, 3 / 2)

Answer 1

a.
`y=x^2-3.8x-0.39`

b.
`y=x^2^ + 100`

c.
`y=x^2 + 4x + 5.5`

Explanation:

Many different graphics can have the same vertex.

The equation of a parabola in the form of a vertex is:

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

where
`(h,k)` is the vertex

• for a.
  `(1.9,-4)`

`h=1.9`

and

`k=-4`

so the equation is:

`y=a(x-1.9)^2+(-4)`

`y=a(x-1.9)^2-4`

As we are not given the value of
`a`, and we are only asked for an equation we can choose the value we like. I will choose a = 1 to simplify

`y=(x-1.9)^2-4`

`y=x^2-3.8x+3.61-4\\y=x^2-3.8x-0.39`

• for b.
  `(0,100)`

`h=0`

and

`k=100`

so the equation is:

`y=a(x-0)^2 + 100`

`y=ax^2+ 100`

again choosing a=1

`y=x^2+100`

• for c.
  `(-2,3/2)`

`h=-2`

and

`k=3/2`

so the equation is:

`y=a(x-(-2))^2+3/2`

`y=a(x+2)^2+3/2`

again choosing a=1

`y=(x+2)^2+3/2`

`y=x^2+4x+4+3/2\\y=x^2+4x+5.5`