SOLUTION: describe the graph of y= -2x^2-6x+5. tell me everything you can about the graph.

Algebra.Com
Question 431081: describe the graph of y= -2x^2-6x+5. tell me everything you can about the graph.
Found 3 solutions by Gogonati, solver91311, ewatrrr:
Answer by Gogonati(855)   (Show Source): You can put this solution on YOUR website!
Solution: represent a parabola which opens down.
The standard form is:
Function, , tell us the vertex (-3/2,19/2) and the
maximum value of y=19/4.
Done.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


It it is a quadratic in x, so it is a parabola with a vertical axis of symmetry.

The lead coefficient is negative, so it opens downward.

The constant term is 5, so the y-intercept is (0,5)

The opposite of the first degree term is 6, divided by 2 times the lead coefficient, is . So the x-coordinate of the vertex is . Substitute for x and then do the arithmetic to calculate the y-coordinate of the vertex.

By symmetry, there is a function value of 5 a distance of horizontally from the vertex, hence (-3,5) is a point on the graph.

Use the discriminant to determine the nature of the zeros.

If there are 1 or 2 real zeros, use the quadratic formula to determine the x-coordinates of the x-intercepts.


John

My calculator said it, I believe it, that settles it
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Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi

y= -2x^2-6x+5

1)parabola opening downward

y=-2(x+3/2)^2 +19/2

2) vertex Pt(-1.5,9.5)

3) cross the y-axis at Pt(0,9.5)

4) Axis of symmetry is x = -1.5

5) 9.5 is the maximum value of y when x = 1.5

6) x = -3/2 ħsqrt(4.75) are the solutions    | (x+3/2) = ħsqrt(19/4)

7) x-intercepts are (.679,0) and (-3.68,0)



 

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