Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form.
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To write the equation of the parabola in vertex form, we need to use the formula
y = a(x – h)^2 + k
where (h, k) is the vertex of the parabola.
Given that the vertex is (5, -3), we have h = 5 and k = -3.
So far, we have the equation in the form y = a(x – 5)^2 - 3.
Now, we need to use the point (6, 1) to solve for a.
Plugging in the values x = 6 and y = 1 into the equation, we get:
1 = a(6 – 5)^2 - 3
1 = a(1)^2 - 3
1 = a - 3
a = 4
Now that we have found the value of a, the equation of the parabola in vertex form is:
y = 4(x – 5)^2 - 3