SOLUTION: Write the quadratic function in vertex form. y = x^2 + 16x + 74

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Question 1100969: Write the quadratic function in vertex form.
y = x^2 + 16x + 74
Found 2 solutions by algebrahouse.com, greenestamps:
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x-coordinate of the vertex.
-b/2a = x-coordinate of vertex

y = x² + 16x + 74
a = 1, b = 16, c = 74

-b
--- = -16/2(1) = -8
2a

x-coordinate of vertex is -8

Find the y-coordinate of the vertex by substituting -8 in for x.

y = (-8)² + 16(-8) + 74 {substituted -8 in for x}
y = 64 - 128 + 74 {evaluated exponent and multiplied}
y = 10 {added and subtracted}

Vertex is (-8,10)

Vertex form is y = a(x - h)² + k
(h,k) are the coordinates of the vertex.

y = (x - 8)² + 10 {substituted vertex into vertex form}

For more help from me, visit: www.algebrahouse.com

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

Vertex form is
y+=+a%28x-h%29%5E2%2Bk

The vertex is at (h,k); the parabola opens upward if a>0 or downward if a<0.

You need to complete the square in x in order to be able to write the equation in that form.

Note the leading coefficient of 1 makes this example easier; we know immediately that the coefficient a in the vertex form is 1, so we can ignore it. Then
y+=+x%5E2%2B16x%2B74
y+=+%28x%5E2%2B16x%29+%2B+74
y+=+%28x%5E2%2B16x%2B64%29+%2B+74+-+64 [complete the square; half of 16 is 8; 8 squared is 64. Then since you added 64 inside the parentheses you need to subtract 64 outside]
y+=+%28x%2B8%29%5E2%2B10

This is vertex form. The vertex (minimum value of the function) is at (-8,10).