Can someone give example for parabole questions ?? Plss i am bad at math

Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2)

lesya692 [45]

Answer:

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Step-by-step explanation:

we know that

The equation of the given parabola is

$(y-k)=a(x-h)^{2}$

we have

the vertex is the point (5,-4)

substitute

$(y+4)=a(x-5)^{2}$

The y-intercept is the point (0,96)

substitute and solve for a

$(96+4)=a(0-5)^{2}$

$100=a(25)$

$a=100/25=4$

The equation of the vertical parabola is equal to

$(y+4)=4(x-5)^{2}$

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

$4=4(x-5)^{2}$

Simplify

$1=(x-5)^{2}$

Rewrite

$(x-5)^{2}=1$

square root both sides

$(x-5)=(+/-)1$

$x=(+/-)1+5$

$x=(+)1+5=6$

$x=(-)1+5=4$

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

4 0

3 years ago

This figure is made up of a rectangle and parallelogram.

ivann1987 [24]

The area of the figure is 40 units. (rounded off from 39.998 units)

Step-by-step explanation:

1. Area of the figure = Area of Rectangle + Area of Parallelogram.

2. Naming points:

Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).

Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).

3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.

In simple words, in A(-6,1), x' = -6; y' = -1

4. Formula for finding area:

Area of a rectangle = length (l) × width (w)

Area of a parallelogram = base (b) x height (h)

5. Finding area of the rectangle:

l = AD = $\sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}$

, i.e. AD = $\sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}$

, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l

Now, w = AB = $\sqrt{[x'' - x']^{2} - [y'' - y']^{2}}$

, i.e. AB = $\sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}$

, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w

Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.

6. Finding area of the parallelogram:

b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)

h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.

Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.

7. Now, adding both, we can arrive at the final answer.

Area of the figure = Area of rectangle + Area of parallelogram,

i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)

4 0

3 years ago

What is the justification for each step in the solution of the equation?

Alexandra [31]

For this case we have the following equation:

$\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\$

If we multiply both sides of the equation by 3 we get:

$2x-1 = 6 (x + 2)$ ---> Multiplication Property of Equality

Applying the distributive property we have:

$2x-1 = 6x + 12$ ---> Distributive Property

Adding 1 on both sides of equality we have:

$2x-1 + 1 = 6x + 12 + 1\\$

$2x = 6x + 13$ ---> Addition Property of Equality

Subtracting $6x$ on both sides we have:

$-6x + 2x = 6x-6x + 13\\$

$-4x = 13$ ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

$\frac{-4x}{-4}= \frac{13}{-4}\\$

$x = -\frac{13}{4}$ ---> Division Property of Equality

5 0

3 years ago

Read 2 more answers

Label the missing side lenght of the figure khan academy

hammer [34]

Answer:

i cant telll bc theres no picture

3 0

3 years ago

¿PLEASE ANSWER ALL FAST?

koban [17]

Answer:

The word "Of" in an equation is interpreted to be multiplication. Also, you must move the decimal two places to the left to change a percent to a decimal.

1. 20 * .12 = 2.4

2. .3 * 70 = 21

3. 300 * .25 = 75 Blue marbles

4. 40 * .35 = $14

8 0

3 years ago