1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
UNO [17]
2 years ago
9

Consider h(x)=x^2+8+15. identify its vertex and y-intercept.

Mathematics
1 answer:
OleMash [197]2 years ago
5 0

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

x = \frac{-b}{2a}

x = \frac{-8}{2(1)}

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

You might be interested in
Help pleaseeee ??????!!!!! I choosed the Death Valley one
disa [49]
1.) C(t) = -0.30(t - 12)^2 + 40
for t = 12: C(12) = -0.30(12 - 12)^2 + 40 = -0.30(0)^2 + 40 = 40°C
For t = 24: C(24) = -0.30(24 - 12)^2 + 40 = -0.30(24 - 12)^2 + 40 = -0.30(12)^2 + 40 = -0.30(144) + 40 = -43.2 + 40 = -3.2°C

4.) F(t) = 9/5 C(t) + 32
for C(t) = 40°C: 9/5 (40) + 32 = 72 + 32 = 104°F
for C(t) = -3.2°C: 9/5(-3.2) + 32 = -5.76 + 32 = 26.24°F

5.) F(t) = 9/5 C(t) + 32 = 9/5 (-0.30(t - 12)^2 + 40) + 32 = -0.54(t - 12)^2 + 72 + 32 = -0.54(t - 12)^2 + 104
5 0
3 years ago
If you multiply 1m times unlimedted what will u get
hjlf

Answer:

∞

simple and correct answer, infinite!

✌️:)

3 0
3 years ago
Read 2 more answers
Please answer fast, this is urgent no explanation need just list answer 1,2,3etc. thanks :)
Sav [38]

Answer:

Hi There!

Step-by-step explanation:

Your Answers Are:

<h3>1: 19.3 CM</h3><h3>2: 273 CM</h3><h3>3: about 45-65 degrees</h3><h3>4: 15 CM</h3><h3>5: 25 CM</h3><h3 /><h3 />

Its hard to work w/o a ruler or a protractor, so these might be incorrect.

If this helps, though, please give me a thanks!! ^^

- abakugosimp

5 0
2 years ago
Determine which function has the greatest rate of change over the interval [0, 2].
ruslelena [56]
Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: m= \frac{y_{2}-y_{1}}{x_2-x_1}

Rate of change of a:
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of a:
m= \frac{y_{2}-y_{1}}{x_2-x_1}
m= \frac{4-1}{2-0}
m= \frac{3}{2}
m=1.5
The average rate of change of the function a over the interval [0,2] is 1.5

Rate of change of b:
Here the end points are (0,0) and (2,2)
m= \frac{2-0}{2-0}
m= \frac{2}{2}
m=1
The average rate of change of the function b over the interval [0,2] is 1

Rate of change of c:
Here the end points are (0,-1) and (2,0)
m= \frac{0-(-1)}{2-0}
m= \frac{1}{2}
m=0.5
The average rate of change of the function c over the interval [0,2] is 0.5

Rate of change of d:
Here the end points are (0,0.5) and (2,2.5)
m= \frac{2.5-0.5}{2-0}
m= \frac{2}{2}
m=1
The average rate of change of the function d over the interval [0,2] is 1

We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>
4 0
3 years ago
Samantha’s annual college tuition is $18,541.89. The college offers a monthly payment plan of 9 equal payments. How much would e
MrRissso [65]
I think 2,057.21 because 18,541.89 divided by 9 is 2,057.21
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the union for two sets a={1,5,8,12,17} and b={5,17}
    9·1 answer
  • Lexi and Maria had $250 altogether. After Lexi spent 2/5 of her money and Maria spent $40 they had the same amount of money left
    14·1 answer
  • Wich is a better deal, a bag of sand witch is 60 pounds for $5 or B a bag of sand witch is $12 for 150 pounds?
    7·1 answer
  • Consider the functions f(x)=3x^2 - 5 and g(x)= √x -5 +2
    15·2 answers
  • What is -2(4g-3)=30 I can't figure it out so I need so help
    15·2 answers
  • Two similar polygons have areas of 4 square inches and 64 square inches.
    11·2 answers
  • I totally need help, (I just wanna see who will join)<br> It works :) <br> kte-diym-hvy
    12·2 answers
  • Jada sister Earns a commission. She makes 3.5 of them out she sells. Last week she sold, 7000 Worth of furniture. How much was h
    10·1 answer
  • I have to turn this in by tonight
    11·1 answer
  • Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter motor company claims tha
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!