All categories

3 years ago

What is the equation, in standard form, of a parabola that models the values in the table?

1 answer:

5 0

f(x) = ax^2 + bx + c

f(0) = ax^2 + bx + c = 5, c = 5
f(-2) = 4a + -2b + 5 = 1 ----------(1)
f(4) =16a + 4b + 5 = -59 ----------(2)
4a -2b = -4
16a + 4b = -64
16a + 4(-2-2a)= -64
16a - 8 - 8a = -64
8a = -56
a = 7
4a - 2b = -4
28 - 2b = -4
b = 16

f(x) = 7x^2 + 16x + 5

You might be interested in

Solve for y. 8y-3y=40

Airida [17]

Answer:

Step-by-step explanation:

8y-3y=40

5y. = 40

y. =8

the value of y is 8.

...

5 0

3 years ago

Read 2 more answers

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

4 years ago

Please help question in the picture

zubka84 [21]

Its 56 I DID this you could only multiple the straight sides

7 0

3 years ago

You and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you

Natali5045456 [20]

I run 1 mile every 6 minutes.
My friend runs 1 mile every 7 minutes.
Lowest Common Multiple: LCM ( 6, 7 ) = 42 minutes.
Me : 42 : 6 = 7 miles
My friend : 42 : 7 = 6 miles.

4 0

3 years ago

Read 2 more answers

Need help with school

Scorpion4ik [409]

Answer:

x = 7.2m

Step-by-step explanation:

Because it is a right triangle, you can use the Pythagorean theorem:

4^2+6^2 = x^2

16+36 = x^2

52 = x^2

sqrt52 = x

7.2 = x

5 0

3 years ago

Read 2 more answers