The graph of a function is a parabola that has a minimum at the point (-3,9). Which equation could represent the function?
1 answer:
Well there are no choices listed so it's going to be hard to say which; we'll write an expression for all of them and then give a few instances.
A parabola with a minimum forms a CUP, concave-up positive, meaning the coefficient a on x² must be positive, a>0.
The general form with vertex (p,q) is
y = a(x-p)² + q
So for us, all our parabolas are of the form
y = a(x- -3)² + 9
y = a(x² + 6x + 9) + 9
y = ax² + 6ax + 9(a+1)
That's the general form for a parabola with vertex (-3,9); a>0 assure the parabola has a minimum at the vertex.
Some instances:
a=1 gives
Answer: y = x²+6x+18
a=4 gives
y = 4x² + 24x + 45
Other positive <em>a</em>s give other possible answers; without the choices it's impossible to know which one they're seeking.
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ANSWER
EXPLANATION
The given equation is
Divide both sides by
Cancel out common factors on the left hand side,
For this solution to be a whole number, then should be a factor of
.
The reason is that, factors of 6 will divide exactly in to 6 without a remainder, making the answer a whole number.
The whole numbers that are factors of 6 are,
Note that, the set of whole numbers are,
{
}
EXPLANATION
The given equation is
Divide both sides by
Cancel out common factors on the left hand side,
For this solution to be a whole number, then
The reason is that, factors of 6 will divide exactly in to 6 without a remainder, making the answer a whole number.
The whole numbers that are factors of 6 are,
Note that, the set of whole numbers are,
{
<h3>Answer: Tony is correct</h3>
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Explanation:
There are number of ways to go about this, but let's pick on the sides marked in the diagram below (circled in red and blue). I picked on those sides specifically because they are on either side of the marked angles (A and Q).
They help form the proportion below, in which we'll show later on its a false statement.
AE/PQ = AB/QR
24/(14.5) = 18/(11.5)
24*11.5 = 14.5*18
270 = 261
We arrive at a false statement at the end, so the original proportion is false. Furthermore, it means the figures are <u>not</u> similar.
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We could try the other way around and try to see if
AE/QR = AB/PQ
is true or not
Let's find out
24/(11.5) = 18/(14.5)
24*14.5 = 11.5*18
348 = 207
We see this is false as well. The gap is even bigger than before, so the first scenario was slightly close to having similar polygons. But neither case works perfectly. So that's why we don't have similar polygons and why Tony is correct. It's not enough to look at the angles only when dealing with polygons that have more than 3 sides. If we were just focused on triangles, then Jacenta would be correct.