1. Warm-up What is the distance formula between two points?
What is the midpoint formula of a segment?
Given P(-5,9) and Q (-8,-7) Find the distance d(P,Q)
… and the midpoint of the segment PQ
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2. Warm-up Answers Distance formula = Midpoint = d(P,Q) = M (-13/2, 1)
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3. Digital Lesson
2.2 Graphs of Equations

4. Example: Sketch the graph of y = –2x + 3.8 4 x 4 4 8 –4
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Example continued

5. Example: Sketch Graph (Quadratic Function)
Example: Sketch the graph of y = (x – 1)2. y x y
(x, y) –2 9
(–2, 9) –1 4
(–1, 4) 1
(0, 1)
(1, 0) 2
(2, 1) 3
(3, 4)
(4, 9) 8 6 2 x –2 2 4
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Example: Sketch Graph (Quadratic Function)

6. Example: Sketch Graph (Absolute Value Function)
Example: Sketch the graph of y = | x | + 1. y x y
(x, y) –2 3
(–2, 3) –1 2
(–1, 2) 1
(0, 1)
(1, 2)
(2, 3) 4 2 x –2 2
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Example: Sketch Graph (Absolute Value Function)

7. Definition of Intercepts
The points at which the graph intersects the x- or y-axis are called intercepts.
If (x, 0) satisfies an equation, then the point (x, 0) is called an x-intercept of the graph of the equation.
If (0, y) satisfies an equation, then the point (0, y) is called a y-intercept of the graph of the equation.
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Definition of Intercepts

8. Example: Find Intercepts
Example: Find the x- and y-intercepts of the graph of y = x2 + 4x – 5.
To find the x-intercepts, let y = 0 and solve for x.
0 = x2 + 4x – 5 Substitute 0 for y.
0 = (x – 1)(x + 5) Factor.
x – 1 = 0 x + 5 = 0 Set each factor equal to 0.
x = x = –5 Solve for x.
So, the x-intercepts are (1, 0) and (–5, 0).
To find the y-intercept, let x = 0 and solve for y.
y = (0) – 5 = –5
So, the y-intercept is (0, –5).
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Example: Find Intercepts

9. Symmetries of Graphs of Equations in x and y
Symmetric with respect to the y-axis: Substitution of –x for x leads to the same equation (This is also called an even function)
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10. Symmetric with respect to the x-axis: Substitution of –y leads to the same equation
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11. Symmetric with respect to the origin: Simultaneous substitution of –x for x and –y for y leads to the same equation (This is also called an Odd function)
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12. Circles Standard Equation of a circle with Center (h, k) and radius r
(x-h)2 + (y-k)2 = r2
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13. Semicircles Top half (solve for y, + √ )
Bottom half (solve for y, - √ )
Right half (solve for x, + √ )
Left half (solve for x, - √ )
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