Question

for a graph of a quadratic i have x intercepts that are x=12 and x =35 do i have enough information to find the y-coordinate of the vertext and why

Answer 1

No... provided no other information or no graph is provided.

Explanation:

You can find the x-coordinate of the vertex which can be calculated using the two given x-intercepts. Using the symmetry of the parabola, it would just mean the vertex should lay midway between the x's. So the x-coordinate of the vertex is (12+35)/2=47/2.

However, we do not have enough information about the relationship between x and y to find the y-coordinate of the vertex.

All we are given is y=a(x-12)(x-35) (where a is real number) since we know the relationship is quadratic, and the zeros are 12 & 35.

So we could have many possible y-coordinates for our vertex since we don't know the value of a in our equation and we can plug in our x-coordinate for our vertex to find them all.

y=a(47/2-12)(47/2-35)

I'm just going to put everything to right of a in calculator:

y=-529/4 ×a

So that's all the possible y-coordinates for the vertex.