What is the vertex of the graph of y = −2x2 − x + 3?

Question

anonymous · Answer

It is a parabola b/c it has a one variable (x) raised to the second power. You need to put the equation in the standard format for a parabola to find the vertex, do you know the standard format?

anonymous · Answer

y=mx+b?

anonymous · Answer

$$Vertex=(\frac{-b}{2a},f(\frac{-b}{2a}))$$
If you have an equation in the form $$y=ax^2+bx+c$$
Your equation is in that form. Can you tell me the values of a, b, and c?

anonymous · Answer

a= -1, b = 1, c = 3

anonymous · Answer

Your equation is $$y=-2x^2-x+3$$, therefore the value of a is actually -2, the value of b is -1, and the value of c is 3, the reason is that your equation is really just:
$$(-2)x^2+(-1)x+3$$

anonymous · Answer

right, because the standard form only has plus signs inbetween the terms.

anonymous · Answer

does this make sense?

anonymous · Answer

Yeah, but that is the original equation? How do I find the vertex.

anonymous · Answer

Ok, good. To find the vertex is easy once you know the values of a,b, and c. The x coordinate of the vertex is just the formula $$\frac{-b}{2a}$$, and the y co-ordinate of the vertex is just the x coordinate plugged into the original equation.

anonymous · Answer

So the x co-ordinate would be (1/(2*-2)) = -(1/4)

anonymous · Answer

Then to find the y coordinate, you just plug in -(1/4) for x into your original equation.

anonymous · Answer

So 25/8?

anonymous · Answer

I got 3.125 by plugging it into my calculator

anonymous · Answer

I need a fraction, it's 25/8

anonymous · Answer

correct

anonymous · Answer

hopefully that works