X=y y=a+b×4 a=15-b b=46-39 find x

Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm

VladimirAG [237]

Answer:

$y=2x^2-4x-8$

Step-by-step explanation:

Factored form of a parabola

$y=a(x-p)(x-q)$

where:

p and q are the x-intercepts.
a is some constant.

Given x-intercepts:

(1+√5, 0)
(1-√5, 0)

Therefore:

$\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))$

$\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})$

To find a, substitute the given point (4, 8) into the equation and solve for a:

$\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8$

$\implies a(3-\sqrt{5})(3+\sqrt{5})=8$

$\implies4a=8$

$\implies a=2$

Therefore, the equation of the parabola in factored form is:

$\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})$

Expand so that the equation is in standard form:

$\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)$

$\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)$

$\implies y=2(x^2-2x-4)$

$\implies y=2x^2-4x-8$

6 0

1 year ago

2x(squared) + 5 - 2 What is the answer to this trinomial?

Juliette [100K]

The answer is 2x + 3.

4 0

3 years ago

Read 2 more answers

All of the equations to –32 = k + –19

soldi70 [24.7K]

Answer:

$k = - 13$

Step-by-step explanation:

$- 32 = k - 19 \\ -32 + 19 = k \\ - 13 = k$

8 0

2 years ago

Stevie and Michael share their profit in a ratio 3:5. Stevie gets £120 more than Michael. How much profit did they make altogeth

Airida [17]

Answer:

£480

Step-by-step explanation:

we can multiply both terms of ratio with same number without changing the ratio.

Example

a:b = ax: bx (here we have multiplied both terms with x)\

Given

Stevie and Michael share their profit in a ratio 3:5

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

3x = 120 + 5x

3x-5x = 120

=> -2x = 120

=> x= -120/2 = -60

As we see profit is negative , hence it cannot be solution.

It can be solved if Stevie and Michael share their profit in a ratio 5:3

(note: in ratio , bigger number should have bigger term in ratio)

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

5x = 120 + 3x

5x-xx = 120

=> 2x = 120

=> x= x120/2 = 60

Profit for stevei = 5x =5*60 = 300

Profit for Michael = 3x = 3*60 = 180

Total profit for them together = 300 + 180 = 480 Answer.

8 0

3 years ago

What is the inverse of the function below? f(x) = 2^x + 6

Helen [10]

The inverse of this function would be f(x) = $\frac{Log(x - 6)}{Log2}$ .

You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.

f(x) = $2^{x}$ - 6 ----> Switch f(x) and x

x = $2^{f(x)}$ - 6 ----> Add 6 to both sides

x + 6 = $2^{f(x)}$ -----> Take the logarithm of both sides in order to get the f(x) out of the exponent

Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2

$\frac{Log(x + 6)}{Log2}$ = f(x) ----> And switch the order for formatting purposes.

f(x) = $\frac{Log(x + 6)}{Log2}$

And that would be your new inverse function.

6 0

3 years ago

Read 2 more answers

X=yy=a+b×4a=15-bb=46-39find x​

X=yy=a+b×4a=15-bb=46-39find x