SOLUTION: Quadratic equation parabola. . y=3-15x-3x^2

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Question 982200: Quadratic equation parabola. .
y=3-15x-3x^2
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
What do you want? Solve, graph, general into standard form, intercepts?

response: most of it.


MISTAKE IS NOW FIXED (it was a mistake in sign.)

COMPLETE REDO----....
y=3-15x-3x%5E2
y=-3%28-1%2B5x%2Bx%5E2%29
y=-3%28x%5E2%2B5x-1%29
Term to complete the square is %285%2F2%29%5E2=25%2F4.
y=-3%28x%5E2%2B5x%2B%285%2F2%29%5E2-25%2F4-4%2F4%29
y=-3%28%28x%2B5%2F2%29%5E2-29%2F4%29
highlight%28y=-3%28x%2B5%2F2%29%5E2%2B87%2F4%29------standard form equation, so now easier to graph.

This is a parabola, concave downward with vertex as a maximum.
The leading coefficient is NEGATIVE, telling you that the vertex will be a maximum. (the negative 3).
Vertex is (-5/2,87/4), which is read directly from the standard form equation.

ROOTS OR ZEROS

-3%28x%2B5%2F2%29%5E2=-87%2F4
%28x%2B5%2F2%29%5E2=87%2F%283%2A4%29
x%2B5%2F2=0%2B-+sqrt%2887%2F3%2A4%29
x%2B5%2F2=0%2B-+%281%2F2%29sqrt%2829%29
highlight%28x=-5%2F2%2B-+%281%2F2%29sqrt%2829%29%29-------the roots, zeros, x-intercepts

y-AXIS INTERCEPT
where x=0
y=3-15x-3x%5E2-----back to the original equation because this will be easier.
y=3-15%2A0-3%2A0%5E2
highlight%28y=3%29--------the y-axis intercept

Graph should look like this:
NOTE: This graph is coded correctly but is not displaying correctly, so
I am not including the rendering tags. Use a graphing tool or such software to
see the graph properly.
graph(300,300,-10,10,-3,24,-3x^2-15x+3)
somewhat different scaling for x versus y axes