Question

Write a quadratic equation to represent a function with the following vertex. Use a leading coefficient

other than 1.
a. (100, 200)
b. (− 3 / 4 , −6)

Answer 1

To write a quadratic equation that represents a function with a given vertex, use the form ax^2+bx+c=0. In case a, the equation is y=4(x-100)^2+200. In case b, the equation is y=2(x+3/4)^2-6.

Step-by-step explanation:

To write a quadratic equation that represents a function with a given vertex, we need to use the form ax^2+bx+c=0. Let's take a look at the two cases:

a. If the vertex is (100, 200), we can write the equation as y=a(x-100)^2+200, where a is a non-zero constant. We can choose a leading coefficient of 4, so the equation becomes y=4(x-100)^2+200.

b. If the vertex is (-3/4, -6), we can write the equation as y=a(x+3/4)^2-6. Let's choose a leading coefficient of 2, so the equation becomes y=2(x+3/4)^2-6.

Answer 2

a.
`y=5(x-100)^2+200`

b.
`y=-2(x+(3)/(4))^2-6`

Step-by-step explanation:

the equation of a quadratic function in the vertex form is:

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

where
`a` is the leading coefficient, and
`(h,k)` is the vertex.

• for a:

we have the vertex
`(100,200)` so
`h=100` and
`k=200`, thus the equation is:

`y=a(x-100)^2+200`

and you can choose any value for
`a` other than 1. I will choose 5:

`y=5(x-100)^2+200`

• for b:

we have the vertex
`((-3)/(4), -6)` so
`h=(-3)/(4)` and
`k=-6`, thus the equation is:

`y=a(x-(-(3)/(4)))^2+(-6)`

`y=a(x+(3)/(4))^2-6`

and you can choose any value for
`a` other than 1. I will choose -2 this time:

`y=-2(x+(3)/(4))^2-6`