Question

1. What are the vertex and the axis of symmetry of the equation?

y = –2x2 + 8x – 18 (1 point)
vertex: ( 2, –10)
axis of symmetry: x = 2
vertex: (2, –10)
axis of symmetry: x = –10
vertex: (–2, –10)
axis of symmetry: x = –2
vertex: (–2, 10)
axis of symmetry: y = –2
4. What is the vertex form of the equation?

y = x2 + 4x – 3 (1 point)
y = (x – 2)2 – 7
y = (x + 2)2 – 7
y = (x – 2)2 + 7
y = (x + 2)2 + 7

Answer 1

5. You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = –0.000475x2 + 0.851x, where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? (1 point)
The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.
The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.
The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.
The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft.

Answer 2

to find the axis if symmetry you use part of the general quadratic formula

\[x = \frac{-b}{2a}\]

in you question you have a = -2 and b = 8

substitute to find the axis of symmetry

the vertex is on the axis of symmetry substitute the axis of symmetry value(x value) into your equation to find the value of y.


The alternative method is to complete the square

the general version of the vertex form is

\[y = a(x - h)^2 + k\]

the vertex is (h, k) and the axis if symmetry is x = h

in your question you have

\[y = -2(x^2 -4x + ? + (9 - ?))\]


you need to find the value of the ? by completing the square.