PLEASE HELP ASAP I DO NOT UNDERSTAND

Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the

maksim [4K]

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

$y=ax^2+bx+c$

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

$x_v=-\frac{b}{2a}$

In this problem, we have:

$y=-x^2-6x-13$

Then:

a = -1

b = -6

We write now:

$x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3$

Part 3:

For this part, we need to find the x-intercepts. This is, when y = 0:

$-x^2-6x-13=0$

To solve this, we can use the quadratic formula:

$x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}$

And solve:

$x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}$ $x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}$

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

Part 4:

To find the y intercept, we need to find the value of y when x = 0:

$y=-0^2-6\cdot0-13=-13$

The y-intercept is at (0, -13)

Part 5:

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

$x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20$ $x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8$

The two points are:

(1, -20)

(-1, -8)

Part 6:

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

$y=-(-3)^2-6(-3)-13=-9+18-13=-4$

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

8 0

10 months ago

A book store is keeping track of the price of books according to the number of pages. Which scatterplot represents

fenix001 [56]

Anyway the answer is 400

8 0

2 years ago

Use the coordinates of the plotted points to complete the calculation below. Pay attention to negative signs.

MArishka [77]

Answer:

3
1
-3
1
-3

Step-by-step explanation:

The change in y is the difference in y-coordinates between the lower right point and the upper left point. Similarly, the change in x is the difference in the x-coordinates of those points.

$\text{Slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{\boxed{3}-6}{2-\boxed{1}}\\\\=\dfrac{\boxed{-3}}{\boxed{1}}\\\\\\=\boxed{-3}$

7 0

3 years ago

Read 2 more answers

Find the average of 8,11,14,13,14, 9,15

drek231 [11]

Answer:

12

Step-by-step explanation:

(8+11+14+13+14+9+15)/7 = 12

8 0

10 months ago

Read 2 more answers

PLEASE HELP

Neko [114]

Answer:

55.5 square feet

Step-by-step explanation:

so the dog house consists of 4 walls, two roof sections, and two triangle bits to make the roof pointy (I'm sure they have a name but I don't know what it is lol) Of the walls there would be 2 of the longer walls and 2 of the shorther ones. Knowing this we just have to add together the area of each part to find the total surface area.

So starting with the walls:

two of them are 4 feet by 2 feet.

The area of a rectangle is just length x width

so those two would have an area of 8 ft^2

and the other two are 3 feet by 2 feet so they would have an area of 6 ft^2

the roof sections are also rectangles with dimensions of 4 feet by 2.5 feet

4x2.5=10 so each side of the roof has a surface area of 10 ft^2

now the triangle parts have a base of 3 feet and a height of 2.5 feet

the formula for area of a triangle is base x height / 2

3x2.5=7.5

7.5/2= 3.75

now we add them together

8+8+6+6+10+10+3.75+3.75=55.5

so the total surface area is 55.5 square ft

8 0

2 years ago