Page 654 - Algebra 1

Step 4: Find one point not on the axis of symmetry. y=x2 +4x+5
y = (1)2 + 4(1) + 5 = 10 Substitute 1 for x.
A point on the curve is (1, 10).
Step 5: Graph.
Graph the axis of symmetry x = -2, the vertex (-2, 1), the y-intercept (0, 5). Reflect the point (1, 10) over the axis of symmetry and graph the point (-5, 10). Connect the points with a smooth curve.
Graphing Quadratics of the Form y = ax2 + bx + c Graph the function.
Hint
Count how far the plotted point (1, 10)
is from the axis of symmetry. Then check that the reflected point is the same distance from the axis of symmetry,
but in the opposite direction.
y
24
16
8
-8
-4
4
Example
2
y=3x2 +18x+13
SOLUTION
Step 1: Find the axis of symmetry.
x = -_b 2a
= -_18 = -3 2(3)
The axis of symmetry is x = -3.
Step 2: Find the vertex.
y=3x2 +18x+13
= 3(-3)2 + 18(-3) + 13 = -14
The vertex is (-3, -14). Step3: Findthey-intercept. The y-intercept is c, or 13.
Use the formula.
Substitute values for b and a.
Substitute -3 for x.
Hint
Identify the values of a, b, and c first.
Step 4: Find one point not on the axis of symmetry. y=3x2 +18x+13
= 3(-1)2 + 18(-1) + 13 = -2 Substitute -1 for x. A point on the curve is (-1, -2).
Step5: Graph.
Graph the axis of symmetry x = -3, the vertex (-3, -14), the y-intercept (0, 13). Reflect the point (-1, -2) across the axis of symmetry to get the point (-5, -2). Connect the points with a smooth curve.
20
x
-6
-4
-2
-10
Lesson 96 639
x