Question

Find the vertex by using the vertex formula. Express numbers in simplest form.m(x)=4x^2-8x-7what is the m and is it separate from the (x) or is it always written m(x)also when I solve this can I change the (x) to an x or does it not matter?

Answer 1

`V=(1,-11)`

1) Considering that the Vertex form of a quadratic equation is given by the following formula:

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

2) We can rewrite that into the Vertex formula noticing that in m(x)=4x²-8x-7, we can find out the vertex by using the Vertex formula for the x-coordinate:

`\begin{gathered} h=(-b)/(2a) \\ h=(8)/(2(4))=1 \end{gathered}`

Now let's plug "1" into the function to get the k value, k is the y-coordinate of the vertex:

`\begin{gathered} m(1)=4(1)^2-8(1)-7 \\ m(1)=4-8-7 \\ m(1)=-11 \end{gathered}`

Notice that since we plugged x=1, then we get the corresponding y-value for that in this case y=-11 and the y-coordinate is the vertex y-coordinate (k)

3) So we can write out the vertex formula of m(x) =4x²-8x-7. Let's pick the vertex formula and plug into that the coefficient "a" and the values for "h" and "k"

`\begin{gathered} y=a(x-h)^2+k \\ y=4(x-1)^2-11 \\ m(x)=4(x-1)^2-11 \end{gathered}`

Note that into this equation m(x) and y are the same thing.