Ask question

Ask question

All categories

3 years ago

12

How would you find the quadratic that goes through the point (4,0), the axis of symmetry is x=7, and it also goes through the po

int (1,5)?

1 answer:

nasty-shy [4]3 years ago

4 0

9514 1404 393

Answer:

y = (5/27)(x -7)^2 -5/3

Step-by-step explanation:

Use the given points to find the unknowns in the equation.

If the axis of symmetry is x=7, then the equation can be written in the form ...

y = a(x -7)^2 +b

Filling in the two point values, we have two equations:

0 = a(4 -7)^2 +b ⇒ 9a +b = 0

5 = a(1 -7)^2 +b ⇒ 36a +b = 5

__

Subtracting the first equation from the second, we have ...

(36a +b) -(9a +b) = (5) -(0)

27a = 5

a = 5/27

Substituting that value into the first equation gives ...

9(5/27) +b = 0

5/3 +b = 0

b = -5/3

So, the quadratic can be written in vertex form as ...

y = (5/27)(x -7)^2 -5/3

You might be interested in

The minimum wage in 2003 was $5.15. This was w more than the minimum wage in 1996. Write an expression for the minimum wage in 1

bekas [8.4K]

$5.15 - w = minimum wage in 1996

(if that wasn't what you were looking for then comment what you really wanted)

8 0

3 years ago

A line has the equation 3x ? 4y = 1. Choose the equation of a line that is parallel to the given line.

cupoosta [38]

Answer:

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Step-by-step explanation:

If the line is 3x - 4y = 1 then the line which is parallel will have the same coefficients of x and y. Parallel lines never cross and to ensure this have the same slope. The slope is a ratio which can be solved for in an equation using the coefficients of x and y. Here the slope is:

3x - 4y = 1

-4y = -3x + 1

y = 3/4x - 1/4.

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

7 0

3 years ago

Read 2 more answers

A circle has a radius of 6. An arc in this circle has a central angle of 330

sashaice [31]

Answer: $Arc\ lenght\approx34.55\ units$

Step-by-step explanation:

<h3> The complete exercise is: " A circle has a radius of 6. An arc in this circle has a central angle of 330 degrees. What is the arc length?"</h3><h3></h3>

To solve this exercise you need to use the following formula to find the Arc lenght:

$Arc\ lenght=2\pi r(\frac{C}{360})$

Where "C" is the central angle of the arc (in degrees) and "r" is the radius.

In this case, after analize the information given in the exercise, you can identify that the radius and the central angle in degrees, are:

$r=6\ units\\\\C=330$

Therefore, knowing these values, you can substitute them into the formula:

$Arc\ lenght=2\pi (6\ units)(\frac{330}{360})$

And finally,you must evaluate in order to find the Arc lenght.

You get that this is:

$Arc\ lenght=2\pi (6\ units)(\frac{11}{12})\\\\Arc\ lenght=11\pi \ units\\\\Arc\ lenght\approx34.55\ units$

3 0

3 years ago

Read 2 more answers

Find all solutions of e^(e^z)=1

den301095 [7]

Start by reviewing your knowledge of natural logarithms. If we take the ln of both sides we get e^z=ln(1). Do the same thing again and wheel about the ln(ln(1)). There's going to be complex solutions, Wolfram Alpah gets them but let me know if you figure out how to do it?

8 0

3 years ago

Which statement describes the inverse of m(x) = x^2 – 17x?

DochEvi [55]

Given:

The function is

$m(x)=x^2-17x$

To find:

The inverse of the given function.

Solution:

We have,

$m(x)=x^2-17x$

Substitute m(x)=y.

$y=x^2-17x$

Interchange x and y.

$x=y^2-17y$

Add square of half of coefficient of y , i.e., $\left(\dfrac{-17}{2}\right)^2$ on both sides,

$x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}$

Add $\dfrac{17}{2}$ on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y$

Substitute $y=m^{-1}(x)$ .

$m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$

We know that, negative term inside the root is not real number. So,

$x+\left(\dfrac{17}{2}\right)^2\geq 0$

$x\geq -\left(\dfrac{17}{2}\right)^2$

Therefore, the restricted domain is $x\geq -\left(\dfrac{17}{2}\right)^2$ and the inverse function is $m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$ .

Hence, option D is correct.

Note: In all the options square of $\dfrac{17}{2}$ is missing in restricted domain.

7 0

3 years ago