SOLUTION: how can I determine if the graph goes upward or downward example y=-2x^2+12x-22

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Question 1111017: how can I determine if the graph goes upward or downward example
y=-2x^2+12x-22
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
If you complete the square, find .

The parabola opens DOWNWARD and maximum point is at (3,-4).

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you look at the coefficient of the x^2 term.

if it is positive, the graph points down and you have a minimum.

if it is negative, the graph points up and you have a maximum.

the graph you showed is y = -2x^2 + 12x - 22.

the graph of this equation points up and will have a maximum.

here's what the graph looks like.

it has a maximum value at (3,-4)

this can be found by using the formula x = -b/2a from the quadratic equation in standard form.

y = -2x^2 + 12x - 22 is in standard form when you set y = 0.

the equation becomes -2x^2 + 12x - 22 = 0

in this form:

a = coefficient of x^2 term = -2
b = coefficient of x term = 12
c = constant term = -22

x = -b/2a becomes x = -12/-4 which becomes x = 3

when x = 3, y = -2x^2 + 12x - 22 = 0 becomes y = -2(3^2) + 12*3) - 22 which becomes y = -18 + 36 - 22 which becomes y = -4

the maximum value of the quadratic equation occurs when x = 3 and y = -4.

that would be the coordinate point of (3,-4) on the graph.

that's what's there, so the algebraic solution confirms the graphical solution.