The Quadratic Formula Solve Quadratic Equations 2 4
- Slides: 16
The Quadratic Formula
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 = 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 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 • 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 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 = 3 and -1 x ints (3, 0) and (-1, 0)
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 = 2 and -7 x ints are (2, 0) and (-7, 0)
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
Practice saying the Quadratic Equation… Sing along with the clip!
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= 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
Can’t have - seconds
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