Download quadratic equation

Solving Quadratic Equations
9-5 by Graphing
Warm Up
1. Graph y = x2 + 4x + 3.
2. Identify the vertex and zeros of the
function above.
vertex:(–2 , –1);
zeros:–3, –1
Holt Algebra 1
Solving Quadratic Equations
9-5 by Graphing
Objective
Solve quadratic equations by graphing.
Holt Algebra 1
Solving Quadratic Equations
9-5 by Graphing
Every quadratic function has a related quadratic
equation. A quadratic equation is an equation
that can be written in the standard form ax2 +
bx + c = 0, where a, b, and c are real numbers
and a ≠ 0.
When writing a quadratic function as its related
quadratic equation, you replace y with 0. So y = 0.
y = ax2 + bx + c
0 = ax2 + bx + c
ax2 + bx + c = 0
Holt Algebra 1
Solving Quadratic Equations
9-5 by Graphing
One way to solve a quadratic equation in standard
form is to graph the related function and find the
x-values where y = 0. In other words, find the
zeros of the related function. Recall that a
quadratic function may have two, one, or no zeros.
Holt Algebra 1
Solving Quadratic Equations
9-5 by Graphing
Solve the equation by graphing the related
function.
2
2
2x – 18 = 0  y  2 x  18
• The axis of symmetry is x = 0.
• The vertex is (0, –18).
• Two other points (2, –10) and
(3, 0)
• Graph the points and reflect them
across the axis of symmetry.
The zeros appear to be 3 and –3.
Holt Algebra 1
3
3,0
 2, 10
Solving Quadratic Equations
9-5 by Graphing
Solve the equation by graphing the related
function.
–12x + 18 = –2x2  2 x 2  12 x  18  0
• The axis of symmetry is x = 3.
• The vertex is (3, 0).
• The y-intercept is 18.
x 3
Holt Algebra 1
6
Solving Quadratic Equations
9-5 by Graphing
Solve the equation by graphing the related
function.
x2
– 8x – 16 =
2x2
 y  x  8 x  16
• The axis of symmetry is x = –4.
• The vertex is (–4, 0).
• The y-intercept is 16.
• Two other points are (–3, 1) and
(–2, 4).
• Graph the points and reflect them
across the axis of symmetry.
The only zero appears to be –4.
Holt Algebra 1
2
 0,16
4
2
Solving Quadratic Equations
9-5 by Graphing
A frog jumps straight up from the ground.
The quadratic function f(t) = –16t2 + 12t
models the frog’s height above the ground
after t seconds. About how long is the frog
in the air?
 0  16t  12t
2
0.75 seconds
0  4t  4t  3
 4t  0 or 4t  3  0
3
 t  0 or t 
4
pp. 625-627/15-29,31,37-43 Odd,49-61 Odd
Holt Algebra 1
1
4