9-4a Solving Quadratic Equations by Graphing - Math Slide Show

Lesson 9-4a
Objective - To find the x-intercepts and to
solve quadratic equations by graphing.
Graph y =−x 2 + 2x+ 8
x y
-3 --3 ( ) 2 + 2-3 ( )+ 8 = -7
-2
--2
( ) 2 + 2 (-2
) + 8 = 0 x-intercepts
-1 --1 ( ) 2 + 2-1 ( )+ 8 = 5
0 -0 () 2 + 20 ()+ 8 = 8
1 -1 () 2 + 21 ()+ 8 = 9
2 -2 () 2 + 22 ()+ 8 = 8
3 -3 () 2 + 23 ()+ 8 = 5
y
x = 1
Vertex
(1,9)
x = -2
x = 4
x
Find the x-intercepts of the equation below.
y = 1 2 x 2 − 4x + 6
Axis
x = −b
= − −4
2a 2 0.5
( )
( )
= 4
Vertex ( 4,y)
y = 1 2 ()2 4 − 44 ()+ 6
y = 8 −16 + 6
y = −2 ( 4,−2)
y
x
Find the x-intercepts of the equation below.
y = 1 2 x 2 − 4x + 6
x-intercepts (set y = 0)
0 = 1 x2 − 4x+ 6
2
Can’t
x = 2
solve
or x
yet!
= 6
x = 2 x = 6
x
solved by graphing
x y
x-intercepts
2 2 − 8 + 6= 0 solutions
6
zeroes
18 − 24 + 6= 0 roots
y
Solve the quadratic equation below by graphing.
x 2 + 2x = 3 Solution: x = -3 or x = 1
−3 − 3
x 2 + 2x − 3 = 0
y
Find x-intercepts of...
y = x 2 + 2x − 3
x
y
-3 (-3) 2 + 2-3 ( )− 3 = 0 x = -3
x = 1
-2 (-2) 2 + 2-2 ( )− 3 = -3
-1 (-1) 2 + 2-1 ( )− 3 = -4
0 ( 0) 2 + 20 ( )− 3 = -3
1 ( 1) 2 + 21 ( )− 3 = 0
2 ( 2) 2 + 22 ( )− 3 = 5
x
Write the quadratic equation you would graph
to solve each quadratic equation below.
1) 5x 2 − 3x − 7 = 0 3) 3x − 2 = x 2
y = 5x 2 −x 2 − x 2
− 3x − 7
−x 2 + 3x − 2 = 0
y =−x 2 + 3x − 2
2) x 2 = 8x 4) 7x 2 =−x + 6
−8x − 8x
−7x 2 − 7x 2
x 2 − 8x = 0
0 =−7x 2 − x + 6
y = x 2 − 8x y =−7x 2 − x + 6
Solve the quadratic equation by graphing.
2
x − 4x = 5 Find the x-intercepts of
2
−5 − 5 y = x −4x −5
2
x − 4x − 5 = 0
y
x = 2
Axis
−b
−( −4)
x
=
=
2a 21 ( )
x = 2
Vertex ( 2, y)
2
y= ( 2) −4( 2)
−5
y= 4−8−5
y 9 2, −9
= − ( )
x
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 9-4a (cont.)
Solve the quadratic equation by graphing.
2
x − 4x = 5 Find the x-intercepts of
2
−5 −5
y = x −4x −5
2
x −4x − 5 = 0
y
x = 2
x = -1 or 5
y-intercept
c=−
5
y− int. =−5
x = -1 x = 5
Other Points
x y
2
solutions
1 () 1 −4()
1 −5
=−8
zeros
2
-1 (-1) −4( -1)
−5
= 0 x-intercepts
2
-2 -2 −4 -2 −5
= 7
roots
( ) ( )
x
2
A kicked soccer ball follows the path y =− x + 12x
where y is the height of the ball and x is its
horizontal distance in meters. Find how far the
ball traveled before it hit the ground. (Hint: y = 0)
Axis
h(x)
−b
−( 12)
36
x = =
32
2a 2 ( −
1
)
28
x = 6
24
Vertex ( 6, y)
20
2
16
y=− ( 6) + 12( 6)
8
y= − 36+
72
4
y 36 6,36
x = 6
= ( )
0 2 4 6 8 10 12 x
2
A kicked soccer ball follows the path y =− x + 12x
where y is the height of the ball and x is its
horizontal distance in meters. Find how far the
ball traveled before it hit the ground. (Hint: y = 0)
y-intercept
c=
0
y− int. = 0
Other Points
x y
2
2 -2 ( ) + 122 ( ) = 20
2
4 -4 + 124= 32
( ) ( )
h(x)
36
32
28
24
20
16
8
4
x = 6
Distance
= 12 m
0 2 4 6 8 10 12
x
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010