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
DaniilM [7]
2 years ago
14

Enter an equation in standard form for the line. Slope is -5, and (-6, -10) is on the line.

Mathematics
2 answers:
murzikaleks [220]2 years ago
7 0
Full detailed explaination!

fredd [130]2 years ago
3 0
Y+10=-5(x+6)
Y +10= -5x-30
5x+y+40=0
You might be interested in
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high sch
galben [10]

Answer:

$1,592.74

Martha will need to pay $1,592.74 more

Step-by-step explanation:

Using the compound interest/inflation formula;

A = P(1+r)^(t)

Where;

A = final value

P = initial value = $10,000

r = inflation rate = 3% = 0.03

t = time = 5 years

Substituting the values;

A = $10,000(1+0.03)^(5)

A = $11592.740743

A = $11,592.74

How much more will Martha need to save;

C = final value - initial value = A - P

C = $11,592.74 - $10,000

C = $1,592.74

Martha will need to pay $1,592.74 more

8 0
3 years ago
What is 78507 divided by 1000?
Romashka [77]
Ur answer is going to be 78.507
3 0
3 years ago
From the diagram, identify a pair of corresponding angles <br><br> i need helppp!
Verizon [17]

Answer:

2 and 6, 1 and 5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A researcher takes a simple random sample of 83 homes in a city and finds that the mean square footage is 1628 with a standard d
8090 [49]

Answer:

Hello

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Classify -2x4 - x 3 + 8x2 = 12 by degree. A. quartic B. quintic C. quadratic D. cubic
    9·1 answer
  • 3a + 21 = 7 - 4a what's the answer
    9·2 answers
  • Suppose f(x)=x^2 and g(x) =7x^2 which statement best compares the graph of g(x) with the graph f(x)
    10·1 answer
  • 3. If the scale factor in a dilation is a number between 0 and
    9·1 answer
  • Bus A and Bus B leave the bus depot at 6 pm. Bus A takes 20 minutes to complete its route once and bus B takes 45 minutes to com
    14·1 answer
  • Which equation shows the relationship between x and y?
    11·2 answers
  • Identify the sampling designs that use voluntary response sampling. Check all that apply.
    6·2 answers
  • F(x)= -2x^2 - 5 and f(2)= -13<br><br> can someone solve this in steps please?
    10·2 answers
  • Seriously need help with this question or I will fail my senior year
    12·2 answers
  • A car is driving at 100kilometers per hour. How far, in meters, does it travel in 2 seconds? Give answer to
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!