Vertex Form Slide 2 Forms of quadratics Factored form a(x-r 1
)(x-r 2 ) Standard Form ax 2 +bx+c Vertex Form a(x-h) 2 +k Slide 3
Each form gives you different information! Factored form a(x-r 1
)(x-r 2 ) Tells you direction of opening Tells you location of
x-intercepts (roots) Standard Form ax 2 +bx+c Tells you direction
of opening Tells you location of y-intercept Vertex Form a(x-h) 2
+k Tells you direction opening Tells you the location of the vertex
(max or min) Slide 4 Direction of opening x 2 opens up Slide 5
Direction of opening ax 2 stretches x vertically by a Here a is 1.5
Slide 6 Direction of opening ax 2 stretches x vertically by a Here
a is 0.5 Stretching by a fraction is a squish Slide 7 Direction of
opening ax 2 stretches x vertically by a Here a is -0.5 Stretching
by a negative causes a flip Slide 8 Direction of opening a is the
number in front of the x 2 The value a tells you what direction the
parabola is opening in. Positive a opens up Negative a opens down
The a in all three forms is the same number a(x-r 1 )(x-r 2 ) ax 2
+bx+c a(x-h) 2 +k Slide 9 Factored form a(x-r 1 )(x-r 2 ) a is the
direction of opening r 1 and r 2 are the x-intercepts Or roots, or
zeros Example: -2(x-2)(x+0.5) a is negative, opens down. r 1 is 2,
crosses the x-axis at 2. r 2 is -0.5, crosses the x-axis at -0.5
Slide 10 Factored form a(x-r 1 )(x-r 2 ) a is the direction of
opening r 1 and r 2 are the x-intercepts Or roots, or zeros
Example: -2(x-2)(x+0.5) a is negative, opens down. r 1 is 2,
crosses the x-axis at 2. r 2 is -0.5, crosses the x-axis at -0.5
Slide 11 Standard form ax 2 +bx+c a is the direction of opening c
is the y-intercept (0)=a0 2 +b0+c=c Example: -2x 2 +3x+2 Opens down
Crosses through the point (0,2) Slide 12 Standard form ax 2 +bx+c a
is the direction of opening c is the y-intercept (0)=a0 2 +b0+c=c
Example: -2x 2 +3x+2 Opens down Crosses through the point (0,2)
Slide 13 Vertex form Start with f(x)=x 2 Slide 14 Vertex form
Stretch/Flip if you want a(x)=ax 2 Slide 15 Vertex form Shift right
by h a(x-h)=a(x-h) 2 h Slide 16 Vertex form Shift up by k
a(x-h)+k=a(x-h) 2 +k h k Slide 17 Vertex form Define a new function
g(x)=a(x-h) 2 +k (h,k) Slide 18 Vertex form a(x-h) 2 +k a tells you
direction of opening (h,k) is the vertex (h,k) Slide 19 Vertex form
a(x-h) 2 +k a tells you direction of opening (h,k) is the vertex
Example: -2(x-3/4) 2 +25/8 Opens down Has vertex at (3/4, 25/8)
Slide 20 Vertex form a(x-h) 2 +k a tells you direction of opening
(h,k) is the vertex Example: -2(x-3/4) 2 +25/8 Opens down Has
vertex at (3/4, 25/8) (3/4, 25/8) Slide 21 Switching between forms
Gives you a full picture Example: (x)=-2(x-2)(x+0.5) (x)=-2x 2
+3x+2 (x)=-2(x-3/4) 2 +25/8 are all the same function Opens down
Crosses x axis at 2 and -0.5 Crosses the y-axis at 2 Has vertex at
(3/4, 25/8) Slide 22 Switching between forms Gives you a full
picture Example: (x)=-2(x-2)(x+0.5) (x)=-2x 2 +3x+2 (x)=-2(x-3/4) 2
+25/8 are all the same function Opens down Crosses x axis at 2 and
-0.5 Crosses the y-axis at 2 Has vertex at (3/4, 25/8) Slide 23
Consider the function f(x) = -3x 2 +2x-9. Which of the following
are true? A)The graph of f(x) has a negative y-intercept B) f(x)
has 2 real zeros. C) The graph of f(x) attains a maximum value D)
Both (A) and (B) are true E) Both (A) and (C) are true. Slide 24
Consider the function f(x) = -3x 2 +2x-9. Which of the following
are true? Standard form: ax 2 +bx+c. a is negative: opens down. (x)
attains a maximum value. (C) is true. c is my y-intercept. c is
negative. My y-intercept is negative. (A) is true. E) Both (A) and
(C) are true. Slide 25 Slide 26 Slide 27 Slide 28 Slide 29 Slide 30
The Vertex Formula Remember the Quadratic formula Slide 31 What
does the QF say? Slide 32 The Vertex Formula Slide 33 Example Slide
34 Given the function R(x)=(2x+6)(x-12), find an equation for its
axis of symmetry. A)x = - 9 B)x = 9 C)x = 2 D)x = 6 E)None of the
above. Slide 35 Given the function R(x)=(2x+6)(x-12), find an
equation for its axis (line) of symmetry. The roots are x=-3 and
x=12. The axis of symmetry is halfway between the roots.
(12-3)/2=4.5, the number halfway between -3 and 12. x=4.5 is the
axis of symmetry E) None of the above. Slide 36 How to find an
equation from vertex and point A parabola passes has its vertex at
(1,3) and passes through the point (0,1). What is the equation of
this parabola? Slide 37 How to find an equation from vertex and
point A parabola passes has its vertex at (1,3) and passes through
the point (0,1). What is the equation of this parabola? (h,k)=(1,3)
(x 1,y 1 )=(0,1) Slide 38 How to find an equation from vertex and
point A parabola passes has its vertex at (1,3) and passes through
the point (0,1). What is the equation of this parabola? (h,k)=(1,3)
(x 1,y 1 )=(0,1) But to be finished, I need to know a! Use: My
formula is true for every x,y including x 1,y 1 Slide 39 How to
find an equation from vertex and point A parabola passes has its
vertex at (1,3) and passes through the point (0,1). What is the
equation of this parabola? (h,k)=(1,3) (x 1,y 1 )=(0,1) My formula
is true for every x,y; not just x 1,y 1 Slide 40 A quadratic
function has vertex at (0,2) and passes through the point (1,3).
Find an equation for this parabola. A)y = (x+2) 2 B)y = x 2 +3 C)y
= x 2 +1 D)y = x 2 E)None of the above Slide 41 A quadratic
function has vertex at (0,2) and passes through the point (1,3).
Find an equation for this parabola. E
