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Semmy [17]
3 years ago
5

What is the equation of the following graph?

Mathematics
1 answer:
dangina [55]3 years ago
7 0

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}

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