SOLUTION: What is the vertex of the function x2 − 14x − 95 = 0? and What is the vertex of the function 2x2 + 16x + 21 = 0?

Algebra ->  Graphs -> SOLUTION: What is the vertex of the function x2 − 14x − 95 = 0? and What is the vertex of the function 2x2 + 16x + 21 = 0?       Log On


   

Question 403910: What is the vertex of the function x2 − 14x − 95 = 0?
and
What is the vertex of the function 2x2 + 16x + 21 = 0?

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is the vertex of the function x^2 − 14x − 95 = 0?
Complete the square:
x^2+ 14x + 7^2 = 95+7^2
(x+7)^2 = 144
Vertex: (-7,-144)
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and
What is the vertex of the function 2x2 + 16x + 21 = 0?
x = -b/2a = -16*(4) = -4,
f(-4) = 2(-4)^2+16(-4)+21 = -11
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Vertex: (-4,-11)
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The x-coordinate of the vertex of an equation with the form
y+=+ax%5E2+%2B+b%2Ax+%2B+c
Is x+=+-b%2F%282a%29
(a)
y+=++x%5E2+-+14x+-+95
a+=++1
b+=+-14
-b%2F%282a%29+=+-%28-14%29%2F%282%2A1%29
-b%2F%282a%29+=+7
So far I have (7,y)
To find y:
y+=+7%5E2+-+14%2A7+-+95
y+=+49+-+98+-+95
y+=+-144
The vertex is at (7,-144)
The plot is:
+graph%28+400%2C+400%2C+-8%2C+20%2C+-150%2C+10%2C+x%5E2+-+14x+-+95%29+
--------------------
(b)
y+=+2x%5E2+%2B+16x+%2B+21
-b%2F%282a%29+=+-16%2F4
-b%2F%282a%29+=+-4
So far I have (-4,y)
To find y,
y+=+2%2A%28-4%29%5E2+%2B+16%2A%28-4%29+%2B+21
y+=+32+-+64+%2B+21
y+=+-11
The vertex is at (-4,-11)
The plot is:
+graph%28+400%2C+400%2C+-10%2C+2%2C+-12%2C+5%2C+2x%5E2+%2B+16x+%2B+21%29+