The points (-9,0) and (19,0) lie on a parabola. a) Determine an equation for its axis of symmetry. b) The y-coordinate of the vertex is -28. Determine an equation for the parabola in factored form. c) Write your equation for part b) in standard form.

texelaare

texelaare

Answered question

2021-02-15

The points (-9,0) and (19,0) lie on a parabola.
a) Determine an equation for its axis of symmetry.
b) The y-coordinate of the vertex is -28. Determine an equation for the parabola in factored form.
c) Write your equation for part b) in standard form.

Answer & Explanation

hosentak

hosentak

Skilled2021-02-16Added 100 answers

a)We can find the equation for the axis of symmetry which is a horizontal line x=hx=h by finding the average of the x-intercepts:
x=9+192
x=5
b)The vertex is on the axis of symmetry so we know that its xx-coordinate, based on part a), is 5. So, the vertex is at (h,k)=(5,28). Using the x-intercepts, we express the parabola's equation in factored form as follows:
y=a(x(9))(x19)
y=a(x+9)(x19)
To find a, use the vertex (5,−28):
28=a(5+9)(519)
28=a(14)(14)
28=196a
17=a
The resulting factored equation is as follows:
y=17(x+9)(x19)
c) The standard form is y=ax2+bx+c ,simply add to the response from part b):
y=17(x210x171)
y=17(x2)(107)x171x

Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-10Added 2605 answers

Explanation

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