Question

(Algebra II) Standard Form of a Quadratic Function - I'm having trouble with two questions on this quiz? Please don't just give answers, try to explain so I can understand.

1). What are the vertex and the axis of symmetry of the equation? y = –2 x 2 + 8 x – 18

5). The graph below models the acceleration of a car. Interpret the meaning of the vertex.

Answer 1

The vertex of the graph is the point where the line crosses its axis of symmetry.
The axis of symmetry is the line that you could fold the graph on and it would be symmetrical about that line.
In your graph you could fold it on the x=10 line (which is a vertical line (goes up and down)) and the graph would be symmetrical. This is saying that you could technically fold this graph in HALF and it would be 100% symmetrical if you were to fold it on that line.
Therefore your vertex is the point on the graph where your line crosses the axis of symmetry which would be (10,something).
Looking at your graph it is (10,60).
Let me know is you need me to explain further

Answer 2

1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so

-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2

plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10

vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)






5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max