Page 655 - Algebra 1

Graphing Quadratics of the Form y = ax2 + c Graph the function.
y=5x2 +4
SOLUTION
Step 1: Find the axis of symmetry.
x=-_b=-_0 =0 2a 2(5)
The axis of symmetry is x = 0. Step 2: Find the vertex. y=5x2 +4
= 5(0)2 + 4 = 4 Substitute 0 for x. The vertex is (0, 4).
Step 3: Find the y-intercept.
The y-intercept is c, or 4.
Step 4: Find one point not on the axis of symmetry. y=5x2 +4.
= 5(-1)2 + 4 = 9 Substitute -1 for x.
A point on the curve is (-1, 9) 24 Step 5: Graph.
Graph the axis of symmetry x = 0, the vertex (0, 4), the y-intercept (0, 4). Reflect the point (-1, 9) across the axis of symmetry to get the point (1, 9). Connect the points with a smooth curve.
A zero of a function is an x-value for a function where f(x) = 0. It is the point where the graph of the function meets or intersects the x-axis. The standard form of a quadratic equation ax2 + bx + c = 0, where a ≠ 0, is the related equation to the quadratic function. The quadratic equation is used to find the zeros of a quadratic function algebraically. Alternatively, a graphing calculator can help find zeros of a quadratic function.
Finding the Zeros of a Quadratic Function
Find the zeros of the function.
a. y=x2-6x+9
SOLUTION
Use a graphing calculator to graphy=x2 -6x+9.
The zero of the function is 3.
Example
3
Math Language
A zero of a function is another name for an x-intercept of the graph.
Example
4
640 Saxon Algebra 1
y
16
8
O
x
-4
-2
2
4
Graphing Calculator
For help with finding zeros, see graphing calculator keystrokes in Lab 8 on p. 583.