HI I NEED HELP WITH THIS!!! SOMEONE ANSWER ASAP PLS
1 answer:
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Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If , then
.
Let's simplify that.
Distribute with :
Combine the end like terms :
Use identity for
:
Combine like terms and
:
We are given .
So we have that .
The vertex happens at .
Compare to
to determine
.
Let's plug it in.
So the coordinate is 5.
Let's find the corresponding coordinate by evaluating our expression named
at
:
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is where the vertex is
.
Let's put into this form.
We are given .
We will need to complete the square.
I like to use the identity .
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of
which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.
9514 1404 393
Answer:
- ∠PAO = 90°
- ∠APO = 30°
- ∠AOB = 120°
- PB ≈ 8.7
Step-by-step explanation:
A tangent makes a right angle with the radius to the point of tangency. Hence ∠PAO is 90°. The ratio of the short side (OA) of the right triangle OAP to the hypotenuse (OP) is 5 : 10 = 1 : 2. These are the ratios found in a 30°-60°-90° triangle, so we know that ∠APO = 30°.
OP is a bisector of angle APB, so that angle is 60°. Angle AOB is the supplement to angle APB, so ∠AOB = 120°.
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As we said above, triangle OAP is a 30°-60°-90° triangle, so its side lengths have the ratios 1 : √3 : 2. This means PA = PB = 5√3 ≈ 8.7.
