Question

Find B and C so that y=1x^2 +bx+c has vertex (3,8)B=_____C=____What is it asking?I am so confused

Answer 1

Quadratic Function

The general form of a quadratic equation is:

`y=ax^2+bx+c`

Comparing this equation with the given function:

`y=1x^2+bx+c`

It's clear that

a=1

We don't know the values of b and c.

To find them, we use the vertex form of the quadratic equation:

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

Where the point (h,k) are the coordinates of the vertex.

Substituting the coordinates of the vertex (3,8):

`y=a(x-3)^2+8`

Expanding the square and substituting a=1:

`y=x^2-6x+9+8=x^2-6x+17`

The equation is now in standard form, and we can easily identify the values of b and c:

b = -6

c = 17