What's Going On? · PDF fileWhat's Going On? Learning Goal I will understand how to find...
28
Finding the Vertex and yIntercept from Factored Form 1 March 19, 2013 What's Going On? Learning Goal I will understand how to find the zeros or xintercepts of a quadratic equation. Quiz Tomorrow What's My Vertex? Find my Vertex! What's my yIntercept?
Transcript of What's Going On? · PDF fileWhat's Going On? Learning Goal I will understand how to find...
Finding the Vertex and yIntercept from Factored Form
1
March 19, 2013
What's Going On?
Learning Goal I will understand how to find the zerosor xintercepts of a quadratic equation.
Quiz Tomorrow
What's My Vertex?
Find my Vertex!
What's my yIntercept?
Finding the Vertex and yIntercept from Factored Form
2
March 19, 2013
What's my Vertex?
x-value of vertex
y-value of vertex
y = (x - 4)(x - 6)
Finding the Vertex and yIntercept from Factored Form
3
March 19, 2013
What's my Vertex?
x-value of vertex
y-value of vertex
y = (x - 1)(x - 5)
Finding the Vertex and yIntercept from Factored Form
4
March 19, 2013
What's my Vertex?
x-value of vertex
y-value of vertex
y = -(x + 2)(x + 6)
Finding the Vertex and yIntercept from Factored Form
5
March 19, 2013
What's my Vertex?
x-value of vertex
y-value of vertex
y = -(x - 5)(x - 9)
`
Finding the Vertex and yIntercept from Factored Form
6
March 19, 2013
Finding the Vertex of a Parabola given a Factored Form Equation
Step 1: Determine the zeros.
Step 2: Determine the xvalue of the vertex by finding the average of the zeros.
Step 3: Determine the yvalue of the vertex by substituting the xvalue into the original equation and solving for y.
Finding the Vertex and yIntercept from Factored Form
7
March 19, 2013
What's my Vertex?
x-value of vertex
y-value of vertex
y = (x + 2)(x - 4)
Finding the Vertex and yIntercept from Factored Form
8
March 19, 2013
y = (x + 6)(x - 2)What's my Vertex?
x-value of vertex
y-value of vertex
Finding the Vertex and yIntercept from Factored Form
9
March 19, 2013
y = -2(x + 1)(x - 3)
What's my Vertex?
x-value of vertex
y-value of vertex
Finding the Vertex and yIntercept from Factored Form
10
March 19, 2013
y = -2(x + 1)(x - 3)To find the x-value of the vertex of a parabola given in factored form we need to go HALF WAY between the two zeros!
We already knew that these parabolas were "symmetrical". The vertical line of symmetry is called the axis of symmetry
Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
11
March 19, 2013
y = -2(x + 1)(x - 3)x-Value of the Vertex
The zeros are x = 1, +3To find the axis of symmetry, add up the zeros and divide by two!
(1) + (+3)2axis of symmetry =
= +2 2
= 1
Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
12
March 19, 2013
y = -2(x + 1)(x - 3)
y-Value of the Vertex
So the axis of symmetry is x = 1
This means that the xvalue of the vertex is 1!
How can we now find the yvalue of the vertex?
Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
13
March 19, 2013
y = -2(x + 1)(x - 3)
y-Value of the Vertex
If we know the xvalue of the vertex, we can find the yvalue of the vertex by just plugging the xvalue into our equation and solving for y!
This will us that when x is 1 (at the vertex) y is ...
Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
14
March 19, 2013
y = -3(x - 3)(x + 9)Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
15
March 19, 2013
y = 5x(x + 2)Find my Vertex!
Finding the Vertex and yIntercept from Factored Form
16
March 19, 2013
Determine the vertex of each parabola.
y = 2(x - 2)(x - 4)
y = -3(x + 2)(x + 8)
y = -0.5(x - 1)(x + 7)
Find my Vertex!
y = (x + 4)(x + 12)
y = (x - 7)(x - 1)
y = 8(x - 5)(x + 9)
y = 6x(x - 2)
y = -3x(x - 8)
Finding the Vertex and yIntercept from Factored Form
17
March 19, 2013
What's my yIntercept?
If you were given the factored form equation y = (x 4)(x + 3)
and asked to find the yintercept, what would you do?
Remember: the y-intercept is the c-value in a standard form equation (ax2 + bx + c)
Finding the Vertex and yIntercept from Factored Form
18
March 19, 2013
What's my yIntercept?
You could expand (or FOIL) this into standard form and find it that way!
y = (x 4)(x + 3)
Finding the Vertex and yIntercept from Factored Form
19
March 19, 2013
What's my yIntercept?
So the y-intercept is -12....Is there a quicker way?
y = (x 4)(x + 3)
Finding the Vertex and yIntercept from Factored Form
20
March 19, 2013
What's my yIntercept?
y = (x + 5)(x 2)
Finding the Vertex and yIntercept from Factored Form
21
March 19, 2013
What's my yIntercept?
y = (x + 6)(x + 1)
Finding the Vertex and yIntercept from Factored Form
22
March 19, 2013
What's my yIntercept?
y = (x 10)(x 3)
Finding the Vertex and yIntercept from Factored Form
23
March 19, 2013
What's my yIntercept?
y = 2(x + 4)(x 5)
Finding the Vertex and yIntercept from Factored Form
24
March 19, 2013
What's my yIntercept?
y = 2(x + 4)(x 5)
The y-intercept is -40
NOT -20!!
Finding the Vertex and yIntercept from Factored Form
25
March 19, 2013
What's my yIntercept?
y = a(x r)(x s)
To find the y-intercept of a parabola in factored form:
Multiply the a-value by r and s. Be sure to keep the signs as you see them!
Finding the Vertex and yIntercept from Factored Form
26
March 19, 2013
What's my yIntercept?
y = 6x(x 3)
yIntercept =
CAREFUL! When we only have one set of brackets, one of the zeros is actually zero!So be sure to multiply by 0!
Finding the Vertex and yIntercept from Factored Form
27
March 19, 2013
What's my yIntercept?
y = 6x(x 3)If you think about this one, it actually makes sense!
We know that this parabola has an xintercept at 0and at +3.
If x = 0 when y = 0, this parabola must have itsyintercept at 0! A yintercept is the point where the curve crosses the yaxis (where x = 0)!
Finding the Vertex and yIntercept from Factored Form
28
March 19, 2013
Determine the vertex and yintercept of each parabola.
y = 2(x - 2)(x - 4)
y = -3(x + 2)(x + 8)
y = -0.5(x - 1)(x + 7)
y = (x + 4)(x + 12)
y = (x - 7)(x - 1)
y = 8(x - 5)(x + 9)
y = 6x(x - 2)
y = -3x(x - 8)
What's my yIntercept?
