Question

I need help finding an equation for a parabola?

Answer 1

Any equation in which there is a variable raised to the power of 2 will make a parabola

Answer 2

so x^2 + 2x + 4 is an example of a parabola

Answer 3

yeah i know that. but how do you find the dilation and translate it given by the given points shown? @TechnoSoul

Answer 4

@jim_thompson5910 please help!

Answer 5

What is the vertex of the yellow parabola?

Answer 6

@NIIICE: Please find the vertex of the BLUE parabola from the graph. Please also find one other point on this BLUE parabola.

Next, write the standard equation of a parabola that one uses when the vertex is known (as it is known here).

Answer 7

@jim_thompson5910 would the vertex on the yellow parabola be (0,0)?

Answer 8

correct, how about the blue one?

Answer 9

(-3,5)?

Answer 10

correct

Answer 11

to translate from yellow to blue, you just translate the vertex

Answer 12

then you reflect to make sure it's opening downward

Answer 13

how do you translate the vertex?

Answer 14

The yellow parabola has the equation y = x^2

Answer 15

since that's the parent function of a parabola

Answer 16

Start with y = x^2

Shift everything 3 units to the right to get y = (x+3)^2

then shift 5 units up to get y = (x+3)^2 + 5

Answer 17

So the blue equation is of the form

y = a(x+3)^2 + 5

where that 'a' will determine which direction it opens up and how dilated it is

Answer 18

to determine the value of 'a', plug in another point on the blue parabola that is NOT the vertex

so plug in (x,y) = (-4,1) and solve for 'a'