Which statement is correct about the function y = 3x2 + 19x – 14?
2 answers:
You just have to factor the given expression. You do this by factoring the first term and the last term.
3
can only be factored with 3x • x, so let's put that into our parentheses.
(3x ?)(x ?)
Now the last term. -14 can be factored more ways than one. Here are some examples:
-14 <span>• 1
</span>14 <span>• -1
7 </span><span>• -2
-7 </span><span>• 2
We know we can't use the first two since they're not options in this question. We also know the middle term is something quite large, so that number is what should be multiplied by three.
(3x - 2)(x + 7)
Let's test it out. By multiplying the insides, the outsides, and adding them together.
-2 </span><span>• x = -2x
</span>
7 <span>• 3x = 21x
</span>
21x - 2x = 19x
Aha! That is correct! Now that we've gotten that figured out, we can eliminate B and D. But what about the others? Well, I usually just graph out the factors with a calculator and see the zeroes from there, but since I don't have that luxury in this case. I'll have to find out some other way. I would say to multiply the factors by each other and switch the signs (without the x).
7 = -7
-2 x 3 = -
- =
That should be your answer. If you have any questions, let me know.
3
(3x ?)(x ?)
Now the last term. -14 can be factored more ways than one. Here are some examples:
-14 <span>• 1
</span>14 <span>• -1
7 </span><span>• -2
-7 </span><span>• 2
We know we can't use the first two since they're not options in this question. We also know the middle term is something quite large, so that number is what should be multiplied by three.
(3x - 2)(x + 7)
Let's test it out. By multiplying the insides, the outsides, and adding them together.
-2 </span><span>• x = -2x
</span>
7 <span>• 3x = 21x
</span>
21x - 2x = 19x
Aha! That is correct! Now that we've gotten that figured out, we can eliminate B and D. But what about the others? Well, I usually just graph out the factors with a calculator and see the zeroes from there, but since I don't have that luxury in this case. I'll have to find out some other way. I would say to multiply the factors by each other and switch the signs (without the x).
7 = -7
-2 x 3 = -
-
That should be your answer. If you have any questions, let me know.
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Answer: The function is .
Explanation:
It is given that Michael Daniels, is standing on his own 10-yard line. He throws a pass toward the opposite goal line. The football is 2 yards above the ground when the quarterback lets it go.
It follows a parabolic path. Reaching its highest point, 30 yards above the ground. It is caught 50 yards downfield at a point 2 yards above the ground.
So, the initial point is (10,2) and the other point is (60,2).
The height function of a football represents a downward parabola. The maximum point of the function is called vertex. So the vertex is (h,30).
The two point (10,2) and (60,2) have same y-coordinate, therefore the function is maximum at the midpoint of both points.
So, the function is maximum at x=35. Hence the vertex is (35,30)
The standard form of the parabola is,
Where (h,k) is vertex and a is scale factor.
Since vertex is (35,30).
The initial point is (10,2).
So the function of height is.
The graph of the function is shown below.
