Page 686 - Algebra 1

b. -x2-2=0
SOLUTION
Graph the related function f(x) = -x2 - 2.
O
y
x
-4
-2
2
4
axis of symmetry: vertex:
y-intercept:
two additional points:
x = 0
(0, -2)
(0, -2)
(1, -3) and (3, -11)
Reflect these two points across the axis of symmetry and connect them with a smooth curve.
From the graph, it can be seen that there is no x-intercept because the graph does not intersect the x-axis.
There is no real-number solution.
c. x2+16=8x
SOLUTION
Write the equation in standard form.
x2 -8x+16=0
Graph the related function f(x) = x2 - 8x + 16.
-4
-8
-12
Caution
When a parabola does not cross the x-axis, there is no real-number solution to the quadratic equation.
axis of symmetry: vertex:
y-intercept:
two additional points:
x = 4
(4, 0)
(0, 16)
(2, 4) and (3, 1)
Reflect these two points across the axis of symmetry and connect them with a smooth curve.
From the graph, the x-intercept appears to be 4. Check Substitute4forxintheoriginalequation.
x2 -8x+16=0;x=4 (4)2 -8(4)+16 0 16 - 32 + 16 0
0=0 ✓ The solution is 4.
16 12
y
8
4
O
x
2
6
8
Lesson 100 671