SOLUTION: Please help me with this question. Write the quadratic function in the form y=a(x-h) square + k and identify the vertex. y= x square

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Question 316873: Please help me with this question. Write the quadratic function in the form
y=a(x-h) square + k and identify the vertex.
y= x square - 10x + 18
Found 2 solutions by stanbon, tinbar:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Write the quadratic function in the form
y=a(x-h) square + k and identify the vertex.
y= x square - 10x + 18
y = x^2-10x+25 + 18 - 25
y = (x-5)^2 - 7
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Vertex: (5,-7)
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Cheers,
Stan H.
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Answer by tinbar(133) (Show Source):
You can put this solution on YOUR website!
firstly, you should know that the form y =a(x-h)+k directly tells us the vertex (h, k). Also, k is the optimal value, either a min or max depending on 'a' being + or -.
y = x^2-10x+18
y = {x^2-10x} + 18 <- first seperate the constant at the end from the terms that depend on x
next we have to turn {x^2-10x} into {x-?}^2
y = {x-5}^2 - 25. we need - 25 becuase {x-5}^2 expanded becomes x^2-10x+25, note that the +25 is an extra value produced when we completed the square. therefore we have to take it away with - 25 resulting in just the first two terms; x^2-10x, which is what we want.
don forget to add the original 18 constant.
y={x-5}^2 -25 +18
y = {x-5}^2 - 7

SOLUTION: Please help me with this question. Write the quadratic function in the form y=a(x-h) square + k and identify the vertex. y= x square - 10x + 18