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Mathematics
Brett Gordon
22 June, 00:27
Solve y = X^2+8X-3 and find min/max
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Mina Nolan
22 June, 01:53
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Y = x^2 + 8x - 3
The function does not factor so to find the solutions you would have to use the quadratic formula or complete the square.
x^2 + 8x = 3
8/2 = 4
4^2 = 16
add 16 to both sides
x^2 + 8x + 16 = 3 + 16
(x + 4) ^2 = 19
Take the square root of both sides.
x + 4 = + - √19
x = - 4 + - √19 Solutions
Min/Max
Since the leading coefficient is a positive 1, the function will have a minimum value. To find the min, we find the vertex using the formula x = - b/2a
x = - 8/2 = - 4
Now plug - 4 back in to the equation and solve for y.
x^2 + 8x - 3 = y
(-4) ^2 + 8 (-4) - 3 = y
16 - 32 - 3 = y
-19 = y
Vertex (-4, - 19)
The minimum value is - 19 when x = - 4
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