Quadratics
Y=a(x-r)(x-s)
FACTORED FORM
Zeroes Or X-intercepts
Axis Of symmetry
(X=(r+s)/2)
What is the axis of Symmetry? The axis of symmetry is the A line of symmetry for a graph. The two sides of a graph on either side of the axis of symmetry look like mirror images of each other.
How do you figure out the axis of symmetry? well you already know how factored form looks like (y=a(x-r)(x-s). now figure out the AOS you would need to know that
X-intercepts = (s,0)(t,0)
x= s+t
2
Example: y= 2(x-1)(x-5)
x-intercept co-ordinate (1,0) (5,0)
Axis of Symmetry: 3
How did I get this answer? like showed before you need add the two X-intercepts and divide them by 2.
To get the AOS for this equation you would need to
x= (1+5)
2
x=3
Graphing Quadratics:
To find the X-intercepts or the zeros from Factered form you would just need to subsitute The "Y" from the equation into zero and solve. The zeroes in the factor form are the opposite of the r and s in a factor form equation. You can also find this by setting y=0 and then solve by factoring.
Y=a(x-r)(x-s)----------> 0=a(x-r)(x-s)
Optimal value
Ex: y=2(x-2)(x+2)
0=2(x-2)(x+2)
x-2=0 x=2
x+2=0 x=-2
Therefore, the x-interxepts of this equation is x=2, -2.
To find the optimal value or the y-value of the vertex, sub-in the x-value (axis of symmetry) into the original equation and solve for y.
Refer to the example y=2(x-2)(x+2). Sub in the x-value into the original equation.
y=2(0-2)(x+2)
y=2(-2)(2)
y=2(-4)
y=-8
Therefore, the optimal value of equation y=2(x-2)(x+2) is -8.
How to Graph Factored form?
Word Problem Examples
y=a(x-r)(x-s)
The flight of a ball can be determined by the equation h=-10t²+20t+10, where h represents the height of the ball in meters, and t represents the amount of time the ball spends in the air in seconds.
Factor the equation into its factored form, then find the x-intercepts, vertex, and graph the equation.
h=-10t²+15t+10
h=-(10t²-15t-10)
10t 5 -2 1
1t -2 5 -10
h=-(10t+5)(t-2)
0=-(10t+5)(t-2)
0=10t+5
-5=10t
10
-1/2=t
Therefore, the x-intercepts are x= -5/10 and x= 2.
X-Value:
x=2-1/2
2
x=0.8
Y-Value:
y=-(10(0.75)+5)(0.75-2)
y=-(12.5)(-1.25)
y=15.6
Vertex:
(0.8,15.6)