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
Kipish [7]
3 years ago
15

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Check all that apply.

Mathematics
1 answer:
statuscvo [17]3 years ago
7 0

Answer:

A, D, E are true

Step-by-step explanation:

You have to complete the square to prove A.  Do this by first setting the function equal to 0, then moving the 5 to the other side.

x^2-8x=-5

Now we can complete the square.  Take half the linear term, square it, and add it to both sides.  Our linear term is 8 (from the -8x).  Half of 8 is 4, and 4 squared is 16.  So we add 16 to both sides.

(x^2-8x+16)=-5+16

We will do the addition on the right, no big deal.  On the left, however, what we have done in the process of completing the square is to create a perfect square binomial, which gives us the h coordinate of the vertex.  We will rewrite with that perfect square on the left and the addition done on the right,

(x-4)^2=11

Now we will move the 11 back over, which gives us the k coordinate of the vertex.

(x-4)^2-11=y

From this you can see that A is correct.

Also we can see that the vertex of this parabola is (4, -11), which is why B is NOT correct.

The axis of symmetry is also found in the h value.  This is, by definition, a positive x-squared parabola (opens upwards), so its axis of symmetry will be an "x = " equation.  In the case of this type of parabola, that "x = " will always be equal to the h value.  So the axis of symmetry is

x = 4, which is why C is NOT correct, either.

We can find the y-intercept of the function by going back to the standard form of the parabola (NOT the vertex form we found by completing the square) and sub in a 0 for x.  When we do that, and then solve for y, we find that when x = 0, y = 5.  So the y-intercept is (0, 5).

From this you can see that D is also correct.

To determine if the parabola has real solutions (meaning it will go through the x-axis twice), you can plug it into the quadratic formula to find these values of x.  I just plugged the formula into my graphing calculator and graphed it to see that it did, indeed, go through the x-axis twice.  Just so you know, the values of x where the function go through are (.6833752, 0) and (7.3166248, 0).  That's why you need the quadratic formula to find these values.

You might be interested in
4/8 times 3/4 simplified pls and thank you
Ivahew [28]

Answer:

3/8

Step-by-step explanation:

divide out the 4's and you are left with 3/8

3 0
3 years ago
How can you the unit rate on a graph that goes through the origin ?
Nonamiya [84]
It must be about the origin in order to do that
5 0
3 years ago
Abby has 16 grapes Jason has 9 grapes how many more grapes does Abby have than Jason
Novay_Z [31]
Abby has 7 more grapes because 16-9=7 
7 0
3 years ago
Read 2 more answers
Which number would you divide the numerator and the denominator of the first fraction to yield the second fraction?
blondinia [14]

Answer:

the number I would to divide the numerator and denominator is 5/5

8 0
3 years ago
I bought a piggy bank for $5.65. I paid with $10. How much change did I get? pls help i am timed!!!!!!!!! U will be marked brain
ipn [44]

Answer:

4.35

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • A card is drawn at random from a standard 52-card deck. find the probability that the card is not a queen.
    9·1 answer
  • Please help me with this problem​
    12·1 answer
  • Express the given cartesian co-ordinate as polar co-ordinate correct to 2 decimal places a.(3,5) b.(6.18,2.35) c.(-2,4) d.(9.6,-
    9·1 answer
  • 1 + 2a + 3 + 4a + 5 + 6a + ...... + 97 + 98a + 99 + 100a = 0 What does a equal?
    5·1 answer
  • A study was conducted to compare the effect of three diet types on the milk yield of cows (in lbs). The sample size, sample mean
    5·1 answer
  • Write an equation of the line that passes through the given point and is perpendicular to the given line. 1 (-6, -4); y = 3x + 1
    7·1 answer
  • A number p divided by 7 is less than -3​
    5·1 answer
  • What is the solution to the inequality 1 2/3 > r - 7/12
    10·1 answer
  • HELP QUICK PLS Which property is used in the following expression? (4 + 8) + 6 = 4 + (8 + 6) Associatve Property Commutitive Pro
    5·1 answer
  • Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many m
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!