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) (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}
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Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
Vertex form is
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
[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]
This is vertex form. The vertex (minimum value of the function) is at (-8,10).
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