The point E(3, -6) is translated 4 units up. What are the coordinates of the resulting point, E'?

Write the equation of the function whose graph is shown. y = (x + )2 +

Deffense [45]

Quadratic form is given in the form
$y= ax^{2}+bx+c$ , where a, b, and c are constants

We substitute the value (8, 12) and (5,3) in turn

$12= a(8)^{2}+b(8)+c$
$12=64a+8b+c$ ... Equation 1

$3=a(5)^{2}+b(5)+c$
$3=25a+5b+c$ ... Equation 2

Equation 1 - Equation 2 gives
$39a+3b=9$ , we call this Equation 3

We also know that (5, 3) is the turning point of the curve, where the value of $x$ is given by $x=- \frac{b}{2a}$
Substitute $x=5$
$5=- \frac{b}{2a}$
$10a=-b$
$b=-10a$ ... Equation 4

Substitute Equation 4 into Equation 3
$39a+3b=9$
$39a+3(-10a)=9$
$39a-30a=9$
$9a=9$
$a=1$

Now we need to work out the value of $b$ and $c$

Substitute $a=1$ back into equation 4
$-10a=b$
$-10(1)=b$
$b=-10$

Substitute $a=1$ and $b=-10$ into either equation 1 or equation 2

$64a+8b+c=12$
$64(1)+8(-10)+c=12$
$64-80+c=12$
$c=12+80-64$
$c=28$

Hence the equation of the quadratic curve is
$y= x^{2} 10x+28$

8 0

3 years ago

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Show your work plzz :))))

ankoles [38]

Answer:

9/10

Step-by-step explanation:

1/6 hour for 3/20 of his yard

6/6 hour or 1 hour = 6* 3/20 = 9/10 of his yard per hour

Mark as brainliest if this helped

6 0

2 years ago

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Prove that the two circles shown below are similar. (10 points) Circle C is shown with a center at negative 3, 1 and a radius of

Tanya [424]

Answer:

Well, in reality, all circles are similar to each other. They will all have the same angles, and they don't really have side lengths. So, they are similar.

But to PROVE they are similar, we will transform Circle C to match circle E.

Circle C has a center at (-3, 1), and Circle E has a center of (4, 9). For Circle C to have the same center as Circle E, we will translate Circle C 7 units to the right, and 8 units up.

Since Circle C has a radius of 4, and Circle E has a radius of 3, dilate Circle C by a factor of 3/4. That way, the radius is 3 units as well.

And there you go! The two circles will map perfectly on top of each other.

Hope this helps!

5 0

2 years ago

Help! I really need to pass!

Dmitriy789 [7]

Answer:

$\huge{ \boxed{ \bold{ \sf{y = - 2x + 6}}}}$