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trasher [3.6K]
1 year ago
8

Find the vertex of the function h(x) = x2 – 4x – 21

Mathematics
1 answer:
lakkis [162]1 year ago
7 0

Answer: (2, -25)

Step-by-step explanation:

The x coordinate of the vertex is x=-\frac{-4}{2(1)}=2.

When x=2, h(2)=2^2 - 4(2)-21=-25.

So, the vertex is (2, -25).

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Please help me if you know how to do this!
lukranit [14]

Question 21

Let's complete the square

y = 3x^2 + 6x + 5

y-5 = 3x^2 + 6x

y - 5 = 3(x^2 + 2x)

y - 5 = 3(x^2 + 2x + 1 - 1)

y - 5 = 3(x^2+2x+1) - 3

y - 5 = 3(x+1)^2 - 3

y = 3(x+1)^2 - 3 + 5

y = 3(x+1)^2 + 2

Answer: Choice D

============================================

Question 22

Through trial and error you should find that choice D is the answer

Basically you plug in each of the given answer choices and see which results in a true statement.

For instance, with choice A we have

y < -4(x+1)^2 - 3

-7 < -4(0+1)^2 - 3

-7 < -7

which is false, so we eliminate choice A

Choice D is the answer because

y < -4(x+1)^2 - 3

-9 < -4(-2+1)^2 - 3

-9 < -7

which is true since -9 is to the left of -7 on the number line.

============================================

Question 25

Answer: Choice B

Explanation:

The quantity (x-4)^2 is always positive regardless of what you pick for x. This is because we are squaring the (x-4). Squaring a negative leads to a positive. Eg: (-4)^2 = 16

Adding on a positive to (x-4)^2 makes the result even more positive. Therefore (x-4)^2 + 1 > 0 is true for any real number x.

Visually this means all solutions of y > (x-4)^2 + 1 reside in quadrants 1 and 2, which are above the x axis.

5 0
3 years ago
One angle of a triangle measures 65°. The other two angles are in a ratio of 3:20. What are the measures of those two angles?
Nataly_w [17]

Answer:

15° and 100°

Step-by-step explanation:

65 + 3x + 20x = 180

23x = 115

x = 5

3 × 5 = 15, 20 × 5 = 100. So the other two angles measure 15° and 100°.

3 0
2 years ago
A composition that involves a translation and a reflection is called a ____________.
Olegator [25]
I think it is a glide reflection.

8 0
3 years ago
A baker bought 88.9 ounces of coconut. The next day, she used 7.4 ounces of it to make coconut frosting. How much coconut does t
shepuryov [24]

Answer:

81.5 = 82 if ur problem said round it out 82 if not put 81.5

Step-by-step explanation:

4 0
3 years ago
The function is y=6x.<br><br> Find the horizontal asymptote of the curve.
Lynna [10]

Answer:

y=-6x/square root (4x^2-160

Step-by-step explanation:

hope this helps please mark me brainliest

6 0
2 years ago
Read 2 more answers
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