How do I find intercepts, zeros and solutions of different equations and graph them?

How do I find intercepts, zeros and solutions of different equations and graph them? Find x and y intercepts Approximate zeros with calculator Find points of intersection 4. Find solutions algebraically

terminology • zero • solution • x-intercept • root Graphically Algebraically where the graph crosses the x-axis. where the function equals zero. f(x) = 0

Solve Equationsby Factoring • 1. Set the equation equal to zero. • 2. Factor the polynomial completely. • 3. Set each factor equal to zero and solve.

Quadratic Formula:

Notes Solving Absolute Value Equations If |x| = a and a ≥ 0 then there could be two solutions: x = a x = -a If |x| = a and a < 0 then there is no solution.

Practice Solve each Absolute Value Equation: 1. |2x| = 10 2. |3x – 5| = 4 3. 4 + |5x| = 29 4. -2|x+3| = 22

Notes If |x| < a and a ≥ 0, then x < a AND x > -a If |x| > a and a ≥ 0, then x > a OR x < -a Solving Absolute Value Inequalities

Discussion Welcome to the LAND of GOR! LAND = Less than →AND GOR = Greater than → OR

Practice Solve each Absolute Value Inequality: 1. |2x| < 10 2. |3x – 5| > 4 3. 4 + |5x| ≤ 54 4. -2|x + 3| > 10 5. |x - 7| < -4

Warm-UpSession 16 1) Determine any points of intersection y = 8 y = 3x2 + 2x Solve 2) x2 – 14x + 49 = 0 3) 4)

A parenthesis means “do NOT include” A bracket means “INCLUDE this number” (3, 49] means greater than 3 and less than or equal to 49 “not including three but including 49” Interval Notation

Polynomial Functions • Examples • Polynomial functions have NO restrictions on their domain (unless it’s an application problem)

Quadratic Inequalities x2 + 12x + 32 < 0 -x2 – 12x – 32 < 0 -8 < x < -4 x < -8 or x > -4 (-8, -4) (- , -8) U (-4, )

Quadratic Inequalities Critical Number Critical Number Most parabolas can be broken up into 3 sections: 2 outer sections and 1 inner section. A solution set for a quadratic inequality will be either the 2 outer sections or the 1 inner section.

x2 + 12x + 32 > 0 -x2 – 12x – 32 > 0 x < -8 or x > -4 -8 < x < -4 Quadratic Inequalities (- , -8] U [-4, ) [-8, -4]

0 Quadratic Inequalities -(x + 7)2 – 6 < 0 (x + 8)2 + 6 < 0 everywhere No where (- , ) These parabolas are all or nothing.

(x – 2)2 < 0 x = 5 Quadratic Inequalities Critical Number (x – 5)2 > 0 Only at one place Everywhere except 5 x = 2 [2] (-, 5) U (5, ) These parabolas could be all or nothing.

Ex. 5 Solve. Treat as an equation. Solve to find critical numbers. Determine if solution will be 2 outer sections or 1 inner section.

Ex. 5 Solve. Critical Number Critical Number -1 < x < 3 (-1, 3)

Ex. 6 Solve.

How do I find intercepts, zeros and solutions of different equations and graph them?