Converting Quadratic Equations to Standard Form

AI Thread Summary
The discussion focuses on converting the quadratic equation y = x^2 + 8x + 20 into standard form. The correct standard form is derived by completing the square, resulting in y = (x + 4)^2 + 4. This indicates that the parabola has been shifted upward by 4 units and to the left by 4 units from its standard position. The original poster expresses confusion over receiving a wrong answer despite arriving at the correct standard form. They plan to clarify the issue with their teacher, suspecting a potential error in the online submission system.
quickclick330
Messages
82
Reaction score
0
Change the equation to standard form.

y = x^2 + 8x + 20


I thought this was the standard form for parabolas?? I tried this as the answer but it said it was wrong

y = (x+4)^2 +4

Thanks for the help! :-)
 
Physics news on Phys.org
Complete the Square to the general form of the equation (and then undo this) and you will have something which is factorable. For your exercise, you want to add and subtract (8/2)^2 , and I will leave the rest of this for your effort to continue.
 
okay so completing the square gives me

y = x^2 +8x + 20 + 16 - 16
y = (x^2 + 8x +16) + 4
then factor...

y = (x + 4)^2 + 4

which is exactly what I got before?
 
quickclick330 said:
okay so completing the square gives me

y = x^2 +8x + 20 + 16 - 16
y = (x^2 + 8x +16) + 4
then factor...

y = (x + 4)^2 + 4

which is exactly what I got before?

That appears to be correct. That IS the standard form for your equation given in your exercise. The parabola has been shifted upward by 4 units and to the left by 4 units from standard position.
 
okay thanks...I'll ask the teacher then, its an online submission homework so maybe somethings wrong. hopefully.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Conceptual question on equations of the form ##x=ay^2+by+c##
Replies
5
Views
1K
Write the Standard Form of the Equation for this Circle
Replies
16
Views
2K
Standard Form of the Equation of a Circle
Replies
15
Views
4K
Intersection of a circle and a parabola
Replies
5
Views
4K
Solving Linear-Nonlinear Systems
Replies
4
Views
2K
Converting standard to polar form
Replies
6
Views
2K
Help simplifying this algebraic expression please
Replies
4
Views
1K
Changing standard form to slope intercept form.
Replies
4
Views
2K
Finding the focus of a parabola given an equation
Replies
4
Views
2K
Identifying the equation of a parabola
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top