Question

What is the equation of the following graph?

Answer 1

There are a couple of different ways you could do this, but I'll show the simpler way. We will use the formula

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

along with the fact that the vertex has h and k coordinates of 1 and 4 respectively, and that a point on the graph is (3, 5). We could have used any point on the graph where there is a definite integer coordinate pair. We will fill in accordingly and solve for a.

`5=a(3-1)^2+4` and

5 = 4a + 4. If we subtract 4 from both sides we get that
`a=(1)/(4)`. Now we will fill in the formula and expand as needed:

`y=(1)/(4)(x-1)^2+4` and

`y=(1)/(4)(x^2-2x+1)+4`. If we distribute the 1/4 in and then add the constants the final equation for that graph will be

`y=(1)/(4)x^2-(1)/(2)x+(17)/(4)`