Thirty- two divided by the opposite of 4

What is the vertex form of y=2x^2-8x+1

bezimeni [28]

Answer:

$2(x-2)^2-7$

Step-by-step explanation:

$y=2x^2-8x+1$

When comparing to standard form of a parabola: $ax^2+bx+c$

$a=2$
$b=-8$
$c=1$

Vertex form of a parabola is: $a(x-h)^2+k$ , which is what we are trying to convert this quadratic equation into.

To do so, we can start by finding "h" in the original vertex form of a parabola. This can be found by using: $\frac{-b}{2a}$ .

Substitute in -8 for b and 2 for a.

$\frac{-(-8)}{2(2)}$

Simplify this fraction.

$\frac{8}{4} \rightarrow2$

$\boxed{h=2}$

The "h" value is 2. Now we can find the "k" value by substituting in 2 for x into the given quadratic equation.

$y=2(2)^2-8(2)+1$

Simplify.

$y=-7$

$\boxed{k=-7}$

We have the values of h and k for the original vertex form, so now we can plug these into the original vertex form. We already know a from the beginning (it is 2).

$a(x-h)^2+k\\ \\ 2(x-2)^2-7$

6 0

3 years ago

NO LINKS! Please help me with this problem

Viktor [21]

Answer:

x=70, y=55

Step-by-step explanation:

Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.

So using this we can derive the equation: $y+2x-15=180$

The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.

So using these we can derive the equation: $x+2y=180$

So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.

Original Equation:

$x+2y = 180$

Subtract 2y from both sides

$x = 180-2y$

Now let's plug this into the first equation

$y+2x-15=180$

Plug in 180-2y as x

$y+2(180-2y)-15=180$

Distribute the 2

$y+360-4y-15=180$

Combine like terms

$-3y + 345 = 180$

Subtract 345 from both sides

$-3y = -165$

Divide both sides by -3

$y=55$

So we can plug this into either equation to solve for x

$x+2y=180$

Substitute in 55 as y

$x+2(55)=180$

$x+110=180$

Subtract 110 from both sides

$x=70$

5 0

2 years ago

Read 2 more answers

I need help with this (don't answer if you don't know)

SashulF [63]

Answer:

Step-by-step explanation:

Here's a step by step tutorial on your calculator on how to do this.

Hit "stat" then "1: Edit". If there are numbers there, arrow up to highlight L1, or L2, or wherever there are numbers. Hit "clear" then "enter" and the numbers will be gone. In L1, enter the Practice throws values. Press 3 then enter, then 12 then enter, then 6 then enter, etc. til all of them are in L1's column. Then arrow over to L2 and do the same with entering all the Free Throw values.

When you're done, hit "stat" again, then arrow over once to "calc" and #4 should say LinReg. That's a linear regression equation. If you have a TI 83, just hit enter and you'll get the equation in the form y = mx + b. If you have a TI 84 or 84+, you'll need to arrow down to the word "calculate" and then you'll see the equation.

One thing...if you have not turned your diagnostics on, you wont be able to see the coefficient of determination (the r-squared value). To make sure it's on:

Hit 2nd, then 0. You have opened up the catalog which lists every single thing your calculator can do in alphabetical order. The hit the button UNDER the MATH button (x to the negative 1) and scroll down until you see "diagnosticsON" and hit enter twice.

If you need to recall the linear regression equation, hit "stat", then "calc" then either enter or calculate and you'll get the linear equation again and an r value and an r-squared value. The closer that number is to 1, the better the data fits that model. I got that the equation is

y = 2.352x - .852 with an r-squared value of .844

To get the quadratic regression equation, hit "stat" then "calc" then choose #5, QuadReg. Repeat the process to calculate your equation. Mine was

$y=.073x^2+1.205x+2.555; r^2=.855$

And for the exponential regression, choose ExpReg (mine is under 0. Yours may be some other number. Just arrow down til you find it, it's there!) My ExpReg equation was

$y=4.229(1.170)^x; r^2=.833$