Algebra, Help! Find an equation in the form y=a(x-h)^2+k?

Question

The vertex of the parabola is (4.7, 108). The other points are (9.4, 0) and (-9.4, 0). What is the equation? I can't find it! Please help me!

The vertex of the parabola is (4.7, 108). The other points are (9.4, 0) and (-9.4, 0). What is the equation? I can't find it! Please help me!

-=Edit=-
The quadratic equation has to go through the three points. (It's a parabola.)

Answer 1

Hi,

If you have a TI83 calculator, enter the 3 points under STAT as values in L1 and L2. then go to STAT, over to CALC and choose QuadReg

You get y = -1.629696x^2 + 144

If you do it without the calculator, take the equation y=a(x-h)^2+k and fill in your vertex (4.7,108) as h = 4.7 and k = 108. BUT STOP!!! If this is the vertex at (4.7,108) with (9.4,0) as a point 4.7 squares to the right, then there also has to be another point 4.7 squares to the left with a y value of 0, so -4.7,0 is too far away for this to be symmetric. So something on your points is goofed up. You may also have wanted all 3 of these points, but (4.7,108) is a point on the graph, but it's not the vertex. In that case the first equation above is correct.

I hope that helps, but your info is goofed up!

Answer 2

Sort of a weird vertex. Since your equation has 3 parameters, a, h and k, and you have 3 points, you can substitute the (x,y) value of each point into the unsolved equation. For example, the points on the x-axis give you 0 = a (9.4-h)^2 +k
0 = a (-9.4-h)^2 +k
The only way this can "work" is that h=0. (equals+equals)=equals. These two equations provide a in terms of h or vice versa. Your vertex point will give you k and the values of a and h.

Answer 3

The roots are x'= -a million and x" = -5 S = -a million-5 = -6 (S = sum of roots) P = -a million*-5 = 5 (P = manufactured from roots) y = a (x² -Sx + P) As a = a million: y= a million* (x² + 6x + 5) y = x² + 6x + 5 all of us comprehend that: (m+n)² = m² + 2mn + n² m² + 2mn + n² = x² + 6x + 5 m² = x² => m=x 2mn = 6x => 2xn = 6x => n =3 (x+3)² = x² + 6x + 9 subtracting 4 in each and each and every aspect: (x+3)² - 4 = x² + 6x + 9 - 4 (x+3)² - 4 = x² + 6x + 5 So, we've: y= a (x² + 6x + 5) y = a million* (x+3)² - 4 y = (x+3)(x+3) - 4 Kisses from Brazil =**

Answer 4

Ok, first you plug everything in. (a point also)
0=a(9.4-4.7)^2+108
Now you simplify
-108=22.09a
Now you divide -108 by 22.09 you get
a=-4.889090086(approximate)
Yay! I hope it helps!

Answer 5

Woah, I never learned that in Algebra

Answer 6

Shame on you! Do your own homework!

Answer 7

sry i never was good at that stuff