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 $a=\frac{1}{4}$. Now we will fill in the formula and expand as needed:

$y=\frac{1}{4}(x-1)^2+4$ and

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

$y=\frac{1}{4}x^2-\frac{1}{2}x+\frac{17}{4}$