Quadratic Graphs
The number of zeros a quadratic function can have.
0, 1, or 2
Standard form:
y=ax2+bx+c
Find the vertex for:
y=x2+10x+6
(-5, -19)
y=1200(1.3)t
growth or decay
growth
what is slope-intercept form?
y=mx+b
The shape of a quadratic function graphed is called:
a parabola
Vertex form:
y=a(x-h)2+k
Find the zeros for the following:
y=3(x-6)(x+4)
x=6 & x=-4
y=55(0.98)t
Decay
Decay
what does the "b" represent in a linear function?
the y-intercept
The name of the line that divides a quadratic function exactly in half.
The value of "a" for a graph of a quadratic function opening downward.
Negative
What are the coordinates of the y-intercept & vertex for the quadratic function:
y=x2-4x+8
y-intercept: (0,8)
vertex: (2,4)
y=10(1.04)t
a. initial value
b. rate or growth or decay (as a %)
a. 10
4%
what does the "m" represent in a linear function?
the slope
The name of the turning point for a quadratic function.
The vertex.
The "c" value in standard form tells you what characteristic of the graph.
y-intercept
Rewrite in vertex form:
y=x2+12x+32
y=1(x+6)2-4 or
y=(x+6)2-4
y=14000(0.92)t
a. initial value
b. rate or growth or decay (as a %)
a. 14000
b. 8%
rewrite the equation in slope-intercept form:
4x-y=6
y=4x-6
The other two names that x-intercepts can be called.
roots and zeros
what properties does the standard form tell us about parabolas when graphed?
direction it opens "a" & y-intercept "c"
what is the value of h & k?
y=-2(x+5)2-6
h=-5 & k=-6
The first year of a charity walk event had an attendance of 500. The attendance y increases by 5% each year. How many people will attend in the 10th year? Round your answer to the nearest person.
814 people
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service.
c=50h+25