Page 653 - Algebra 1

L E S S O N Graphing Quadratic Functions 96
Warm Up
New Concepts
1. Vocabulary A(n) __________ is a line that divides a figure or graph into
(89)
two mirror-image halves.
Evaluate for the given value.
2. y = 4x2 - 6x - 4 for x = _1 3. y = -x2 + 5x - 6 for x = -2
(9) 2 (9) Find the axis of symmetry using the formula.
4.y=-2x2 +4x-5 5.y=x2 -3x-4 (89) (89)
A quadratic function can be graphed using the axis of symmetry, the vertex, the y-intercept, and pairs of points that are symmetric about the axis of symmetry. The quadratic function in the standard form f(x) = ax2 + bx + c can be used to find these parts of the graph of the parabola.
Math Reasoning
Analyze Why can a not equal 0 in the standard form of a quadratic equation?
Online Connection www.SaxonMathResources.com
a function is the point on the graph where x = 0. For quadratic functions in standard form, the y-intercept is c.
Graphing Quadratics of the Form y = x2 + bx + c Graph the function.
y=x2 +4x+5
SOLUTION
Step 1: Find the axis of symmetry.
x = -_b Use the formula. _2a
4 _4
= - 2 · 1 = - 2 = -2 Substitute values for b and a.
The axis of symmetry is x = -2. Step 2: Find the vertex.
y=x2 +4x+5
= (-2)2 + 4(-2) + 5 = 1 Substitute -2 for x. The vertex is (-2, 1).
Step 3: Find the y-intercept.
The y-intercept is c, or 5.
The equation of the axis of symmetry and the x-coordinate of the vertex of a quadratic function is x = -_b . To find the y-coordinate of the vertex,
2a
substitute the x-coordinate of the vertex into the function. The y-intercept of
Example
1
638 Saxon Algebra 1