Question

Given the vertex (2, -1 )and the point(0,7), write the vertex form equation of the

Answer 1

Answer:

f(x) = 2(x - 2)² - 1

Step-by-step explanation:

Given the vertex, (2, -1) and the point, (0, 7), we can plug these values into the vertex form of the quadratic function:

f(x) = a(x - h)² + h

where:

vertex = (h, k)

a = determines whether the graph opens up or down, and the wideness or narrowness of the parabola.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

We could substitute the given values into the vertex form, and solve for the value of "a":

f(x) = a(x - h)² + h

7 = a(0 - 2)² - 1

7 = a(-2)² - 1

7 = a(4) - 1

Add 1 to both sides:

7 + 1 = a(4) - 1 + 1

8 = 4a

Divide both sides by 4 to solve for a:

8/4 = 4a/4

2 = a

Since a = 2, and the vertex = (2, -1) then we could plug this value into the given function:

f(x) = 2(x - 2)² -1

Attached is a screenshot of the graph where it contains the given points.

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