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
igor_vitrenko [27]
3 years ago
12

Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,4​) and passes through the point ​(−7​,0). Write the function

in standard form.
Mathematics
1 answer:
olganol [36]3 years ago
5 0

Answer:

Step-by-step explanation:

This is a parabola since a quadratic is a parabola.  The standard form for a parabola is y = ax² + bx + c

but before we do that, we will use the vertex form, since it will make our work easier at the beginning.  

First and foremost, when we plot the vertex and the given point, the vertex is higher up than is the point; that means that this parabola opens upside down, and its vertex form will be

y=-|a|(x - h)² + k

The absolute value is out in front of the a, so we know that the value of a is positive, but the quadratic itself is negative (upside down) and we will find that math takes care of that negative that needs to be out front.  So we need to solve for a by filling in the x, y, h, and k values from the point and the vertex:  x = -7, y = 0, h = -3, k = 4

0 = a(-7 - (-3))² + 4 and

0 = a(-7 + 3)² + 4 and

0 = a(-4)² + 4 and

0 = a(16) + 4 and

0 = 16a + 4 and

-4 = 16a so

a=-\frac{1}{4}

Now that we know a, we can plug it back into the vertex form and then put it into standard form from there.

y=-\frac{1}{4}(x+3)^2+4

Now we will FOIL out what's inside the parenthesis to get

y=-\frac{1}{4}(x^2+6x+9)+4

Simplify by distributing the -1/4 into the parenthesis:

y=-\frac{1}{4}x^2-\frac{3}{2}x-\frac{9}{4}+4

Combine like terms to get

y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{7}{4}

And there you go!

You might be interested in
Somebody help me solve;
Nadya [2.5K]
P(at least 5 rolls until 1) = P(4 rolls are not 1) = 5/6 x 5/6 x 5/6 x 5/6 = 0.4823 (4sf)

Fewer than 7 rolls to get second 1 after first takes 3 rolls means second occurs on 4th, 5th or 6th roll
The probability of each of these is 1/6, 5/6 x 1/6 and 5/6 x 5/6 x 1/6 respectively.
P(second 1 on 4th, 5th or 6th roll) = 1/6 + 5/36 + 25/216 = 91/216 = 0.4213 (4sf)
3 0
2 years ago
Write an equivalent expression for 20(x-5)
mamaluj [8]

Answer:

40(x-10)

Step-by-step explanation:

5 0
3 years ago
If you know the answer for this please help me I would really appreciate it thank you!
STALIN [3.7K]

Answer:

  line QR

Step-by-step explanation:

Plane QRB is the front face. Plane TSR is the top face. The planes intersect at the top front edge, line QR.

3 0
3 years ago
Mr Wallace sells appliances in receives a weekly salary of $275 plus a 3% Commission on all of his self last week is sells total
Greeley [361]

Answer:

The total earning of Mr Wallace for the week is $310.37  

Step-by-step explanation:

Given as :

The fixed weekly salary of Mr Wallace = $275

And The commission of 3% on his total sell

Last week Mr Wallace total sells amount= $1179

I.e 3% of total sells amount = 3% of $1179 = .03 × $1179 = $35.37

∴The total earning = $275 + $35.37 = $310.37

Hence The total earning of Mr Wallace for the week is $310.37    Answer

8 0
3 years ago
PLZ HELP!!!!!!<br>PLZ IM Begging <br>I will give BRAINLIST if correct
ira [324]

Answer:

The answer is A

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • The image below shows two parallel lines cut by a transversal. What is the value of A
    12·1 answer
  • Can two obtuse angles be complementary
    8·1 answer
  • If a and b are independent events then it must be true that P(A|B)=P(A). TRUE OR FALSE.
    9·2 answers
  • I need help is it A B C Or D
    14·1 answer
  • Given the sides 4, 6, 12, what type of triangle is this
    5·1 answer
  • For each function, what is the output of the given input? for f(x) = 4x 7, find f(4)
    7·1 answer
  • Write a ratio in three ways, comparing the first quantity to the second.
    6·1 answer
  • Can someone please help me with math
    9·1 answer
  • How do you expand -10(4-b)
    5·1 answer
  • PLS HELP QUICK!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!