The Quadratic Formula Solve Quadratic Equations 2 4

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The Quadratic Formula

The Quadratic Formula

Solve Quadratic Equations: 2 4 x - 100 = 0 4 x 2 =

Solve Quadratic Equations: 2 4 x - 100 = 0 4 x 2 = 100 2 x = 25 x = ± 5 In this problem, you can solve for x with inverse operations and simply using a square root

Solve Quadratic Equations: But What about… 2 -x = -2 x - 3 0

Solve Quadratic Equations: But What about… 2 -x = -2 x - 3 0 = x 2 -2 x - 3 We can’t combine like terms when there is an x 2 and x term – need to use a new formula!

Quadratic Formula: To Solve Use the Quadratic Formula: 1. write the equation in standard

Quadratic Formula: To Solve Use the Quadratic Formula: 1. write the equation in standard form 2. set the function equal to 0 3. Plug in a, b, and c values and simplify

Quadratic Equation Solutions: • You could get two solutions, one solution, or no solutions

Quadratic Equation Solutions: • You could get two solutions, one solution, or no solutions • The solutions are the x intercepts (called “zeros” or “roots” of the function) • Plugging in a 0 for the y (set the equation = 0) gives x intercepts

Use Quadratic Formula to Solve: Ex. 1 2 y-x = -2 x-3 +x 2

Use Quadratic Formula to Solve: Ex. 1 2 y-x = -2 x-3 +x 2 1. Write in standard form y=ax 2+bx+c y= -2 x - 3 0 = x 2 -2 x - 3 2. Make sure function is set = 0 (This is standard form a=1 b=-2 c=-3 3. Plug in a, b, c values and simplify Work continued… x 2 with a 0 instead of y)

Use Quadratic Formula to Solve: Plug in a=1 b=-2 c=-3, and simplify x =

Use Quadratic Formula to Solve: Plug in a=1 b=-2 c=-3, and simplify x = 3 and -1 x ints (3, 0) and (-1, 0)

Use Quadratic Formula to Solve: Ex. 2 x 2+5 x = 14 1. Write

Use Quadratic Formula to Solve: Ex. 2 x 2+5 x = 14 1. Write in standard form y=ax 2+bx+c x 2+5 x-14 2. Make sure function is set = 0 (This is standard form -14 =0 with a 0 instead of y) a=1 b=5 c=-14 3. Plug in a, b, c values and simplify Work continued…

Use Quadratic Formula to Solve: Plug in a=1 b=5 c=-14, and simplify x =

Use Quadratic Formula to Solve: Plug in a=1 b=5 c=-14, and simplify x = 2 and -7 x ints are (2, 0) and (-7, 0)

Ex. 3 Solve: Clear out - in front of a by multiplying both sides

Ex. 3 Solve: Clear out - in front of a by multiplying both sides by -1 0= 2 x +2 x-5

Rationalize answer if not perfect squares

Rationalize answer if not perfect squares

Practice saying the Quadratic Equation… Sing along with the clip!

Practice saying the Quadratic Equation… Sing along with the clip!

REAL LIFE: 1050 ft. If you throw a rock straight down from a cliff

REAL LIFE: 1050 ft. If you throw a rock straight down from a cliff at a speed of 30 ft. /sec. , how soon will it hit the ground?

Formula: h=-16 t 2+vt+s h= height at time t t= time in seconds s=

Formula: h=-16 t 2+vt+s h= height at time t t= time in seconds s= starting height in feet v= velocity (ft/sec. ) falling is Set h=0 when rock hits ground 2 0=-16 t +vt+s 2 0=-16 t +(-30)t+1050

And

And

Can’t have - seconds

Can’t have - seconds