Identify the range of the equation y = −x2 − 8x − 10.

All real numbers

y ≥ −2

y ≤ 6

y ≤ −4
@cwrw238

Question

Identify the range of the equation y = −x2 − 8x − 10.

 All real numbers

 y ≥ −2

 y ≤ 6

 y ≤ −4
@cwrw238

anonymous · Answer

is  it suppose to be -x^2

anonymous · Answer

it's suppose to be the range not the solution.

debbieg · Answer

is it: $y=-x^2-8x-10$?

debbieg · Answer

I'm assuming so - so what do you know about the range of a quadratic?

anonymous · Answer

yes it is and that is my mistake I very sorry. This is a pre-assessment to a new module.

debbieg · Answer

OK, so what do you know about the range of a quadratic function?

anonymous · Answer

I don't have a clue to what it is or even how or work it.  :D

debbieg · Answer

What do you know about quadratic functions? (e.g., equations of the form $y=ax^2bx+c$?

Do you know what shape the graph of such a function is?

Do you know what the range of a function is?

debbieg · Answer

oops, sorry that should be $$y=ax^2+bx+c$$up there.

anonymous · Answer

I know its a parabola and it open downwards, Correct?

debbieg · Answer

Yes, good! Now, do you know how to find the vertex?

anonymous · Answer

I guess that the range is inside the side that the parabola opens.

debbieg · Answer

Hmmmm.... no, the range of a function (in general) is all of the possible y values that the function can take on. In terms of a graph, you can "see" the range as all the values of y that have a point on the graph associated to them.

debbieg · Answer

So, e.g., if the function was y=x^2, the most basic quadratic, it would have its vertex at (0,0) and open up. So for every point on the graph, $y\ge0$ so that is the range.

anonymous · Answer

Ok well how do I find the vertex?

debbieg · Answer

So for a parabola, if you know the vertex and direction of opening, you know the range - see? Because the y of the vertex is either the lower bound of the range (if it opens upward) or the upper bound (if it opens downward).

anonymous · Answer

So since it opens downwards it would be less than or equal too?

debbieg · Answer

There are several different ways. :) If all you need is the range, I would probably use the formula $\large x=\dfrac{-b}{2a}$ to find the x-coordinate of the vertex. Once you have that, plug it back into the equation, and that will give you the y coordinate of the vertex.

debbieg · Answer

Yes, since it opens down, it will be a less than expression. :)

anonymous · Answer

Ok which one is b and which one is a?

anonymous · Answer

@cwrw238

debbieg · Answer

Like I said above, the equation is of the form $y=ax^2+bx+c$. So you tell me: what is a, what is b?