Question

Avery and Bailey are reviewing equations of parabolas for their upcoming math test. They disagree on what the equation would look like for a parabola with a vertex at (4, -3) a. Help them write an equation for a parabola that opens upward from its vertex at (4, -3). What is the equation of its line of symmetry?b. Zane wants the same parabola to open down and Liz wants it to be stretched vertically. Show them how to change your original equation to meet both of their desires. Does the line of symmetry change? c. Move your parabola from part (b) 4 units to the right and 2 units down and compress it vertically. What is the equation of the parabola? What is the equation of its line of symmetry?

Answer 1

1) Since the vertex is at (4,-3) then the line of symmetry is a vertical line that intercepts and divides the parabola in the "middle"

It's given by the x-coordinate of that Vertex

a) Then the equation of its line of symmetry is going to be

x=4

b) Taking y=x² as our parent function.

Zane will need to multiply the y=x² by -1 to get y=-x²

Since Liz wants to stretch that She needs to increase the coefficient of a by multiplying it by 2, 3, etc.. to get for example y=2x², y=3x², and so on

c) To move the parabola 4 units to the right we need to subtract four units.

y=x²-4

And then, finally 2 units down

y=(x-4)²-2 The equation of the parabola

The equation of the line of symmetry is given by -b/2a the X-coordinate at the vertex

Xv= 8/2= 4

So x=4 Equation of the line of symmetry