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
Sidana [21]
3 years ago
8

Graph the line and the parabola and find the points of intersection: y= 3-x ; y=x(squared)+x-12

Mathematics
1 answer:
melomori [17]3 years ago
4 0

Answer:

Step-by-step explanation:

We have to graph a line y = 3 - x which has the slope = -1 and y intercept 3.

We will select two points where line intersects at x = 0 and y = 0

The given line will intersect x-axis at (3, 0) and at y- axis (0, 3).

Joining these two points we can draw a straight line showing y = -x + 3

Now we will draw the parabola given by equation y = x² + x - 12

We will convert this equation in vertex form first to get the vertex and line of symmetry.

Standard equation of a parabola in vertex form is

y = (x - h)² + k

Where (h, k) is the vertex and x = h is the line of symmetry.

y = x² + x - 12

y = x² + 2(0.5)x + (0.5)²- (0.5)²-12

y = (x + 0.5)² - 12.25

Therefore, vertex will be (-0.5, -12.25) and line of symmetry will be x = 0.5

For x intercept,

0 = (x + 0.5)² - 12.25

x + 0.5 = ±√12.25

x = -0.5 ± 3.5

x = -4, 3

For y- intercept,

y = (0+0.5)² - 12.25

 = 0.25 - 12.25

y = -12

So the parabola has vertex (-0.5, - 12.25), line of symmetry x = 0.5, x intercept (4, 0), (and y-intercept (0, -12).

Now we have to find the points of intersection of the given line and parabola.

For this we will replace the values of y

3 - x = x² + x - 12

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

x = 3, -5

For x = 3

y = 3- 3 = 0

For x = -5

y = 3 + 5 = 8

Therefore, points of intersection will be (3, 0) and (-5, 8)

 

You might be interested in
The sum of the exterior angles of an octagon is 360 degrees. True False
NeX [460]
The answer is true duh
4 0
3 years ago
Read 2 more answers
I FORGOT THE LAST ONE
zalisa [80]
I think it’s 3.2 but I don’t know
5 0
3 years ago
Read 2 more answers
18.) A cylinder and a cone have the same radius and<br> the same volume. How do the heights compare?
mart [117]

Answer:

If a cone and a cylinder have the same base and the same height, then the volume of the cone is of the volume of the cylinder. For example, the cylinder and cone shown here both have a base with radius 3 feet and a height of 7 feet. The cylinder has a volume of cubic feet since .

Step-by-step explanation:

6 0
2 years ago
How do I simplify this expression?
Novay_Z [31]
Her go your answer!

7 0
3 years ago
The functions f (x) = 1/2x-3 and g(x) = -2x+ 2 intersect<br> at x = -2. True or false?
Norma-Jean [14]

9514 1404 393

Answer:

  False

Step-by-step explanation:

f(-2) = (1/2)(-2) -3 = -1 -3 = -4

g(-2) = -2(-2) +2 = 4 +2 = 6

The function values are not the same at x=-2, so the graphs do not intersect there.

__

The graphs intersect at x=2.

4 0
3 years ago
Other questions:
  • Determine weather each table represents a linear, quadratic, or exponential function.
    9·1 answer
  • I need to understand the solution.
    15·1 answer
  • Factor x2 – 6x – 7.
    9·1 answer
  • If ​f(x)equals 2xminus5 and ​j(x)equals ​f(x)plus3​, write the equation for​ j(x).
    7·1 answer
  • Factor completely. x^2−3x−40
    8·1 answer
  • A line is perpendicular to y = - x - 2 and intersects the point (-5, 10)
    5·1 answer
  • Find the value of x.<br> х<br> 50°
    10·1 answer
  • Mark each of the following as true or false and explain how you know.
    8·2 answers
  • 2500 principal earning 4%, compounded quarterly, after 4 years.
    6·1 answer
  • Watch help videoA shipping container will be used to transport several 50-kilogram crates across thecountry by rail. The greates
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!