Page 684 - Algebra 1

L E S S O N Solving Quadratic Equations by Graphing 100
Warm Up
1. Vocabulary The U-shaped curve that results from graphing a quadratic
(84)
function is called a(n) . Evaluate each expression for the given values.
2. 3(x - y)2 - 4y2 for x = -5 and y = -2 (9)
3. -x2 - 3xy + y for x = 3 and y = -1 (9)
Determine the direction that the parabola opens.
4.f(x)=3x2 +x-4 5.f(x)=-2x2 +x+1
(84) (84)
The solution(s) of a quadratic equation, 0 = ax2 + bx + c, can be found by graphing the related function, f(x) = ax2 + bx + c. The U-shaped graph
of a quadratic function is called a parabola. The solutions of the equation are called roots and can be found by determining the x-intercepts or zeros of the quadratic function. These zeros can be found by graphing the related function to see where the parabola intersects the x-axis.
New Concepts
Math Language
The same function is described by
y = 3x2 - 5
and f(x) = 3x2 - 5.
The function notation for y is f(x). It is read, “f of x.”
Graphical Solutions
y
4
2
O
x
-2
2
4
6
One Real Solution
The graph intersects the x-axis at the vertex.
Two Real Solutions
The graph intersects the x-axis at two distinct points.
2
y
4
x
O
4
-2
-4
No Real Solutions
The graph does not intersect the x-axis.
-2
-4
-6
y
2
4
6
x
O
Online Connection www.SaxonMathResources.com
Lesson 100 669