1. Objective
Solve quadratic equations by graphing.

2. Lesson Quiz: Part I
1. Order the function f(x) = 4x2, g(x) = –5x2, and h(x) = 0.8x2 from narrowest graph to widest.
2. Graph of f(x) = x2 and g(x) =0.5x2 –2 on the same graph. How are they different/the same?
g(x) = –5x2, f(x) = 4x2, h(x) = 0.8x2
The graph of g(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 0.
The vertex of g(x) is (0, –2); the vertex of f(x) is (0, 0).

3. Example 1A: Solving Quadratic Equations by Graphing
Solve the equation by graphing the related function.
2x2 – 18 = 0
Step 1 Write the related function.
2x2 – 18 = y, or y = 2x2 + 0x – 18
Step 2 Graph the function.
x = 0 ● ●
The axis of symmetry is x = 0.
The vertex is (0, –18).
Two other points (2, –10) and
(3, 0)
Graph the points and reflect them
across the axis of symmetry.
(3, 0) ● ●
(2, –10) ●
(0, –18)

4. Example 1A Continued
Solve the equation by graphing the related function.
2x2 – 18 = 0
Step 3 Find the zeros.
The zeros appear to be 3 and –3.
Check 2x2 – 18 = 0
2(3)2 –
2(9) –
18 – 
2x2 – 18 = 0
2(–3)2 –
2(9) –
18 – 
Substitute 3 and –3 for x in the quadratic equation.

5. Example 1B: Solving Quadratic Equations by Graphing
Solve the equation by graphing the related function.
–12x + 18 = –2x2
Step 1 Write the related function.
y = –2x2 + 12x – 18
x = 3
Step 2 Graph the function.
(3, 0) ● ● ●
The axis of symmetry is x = 3.
The vertex is (3, 0).
Two other points (5, –8) and
(4, –2).
Graph the points and reflect them
across the axis of symmetry.
(4, –2) ●
(5, –8) ●

6. Example 1B Continued
Solve the equation by graphing the related function.
–12x + 18 = –2x2
Step 3 Find the zeros.
The only zero appears to be 3.
Check
y = –2x2 + 12x – 18
0 –2(3)2 + 12(3) – 18
0 – – 18 
You can also confirm the solution by using the Table function. Enter the function and press When y = 0, x = 3. The x-intercept is 3.