The Quadratic Formula

Solve Quadratic Equations: What about… 4x2 - 100 = 0 -x2 = -2x - 3 4x2 = 100 x2 = 25 We can’t combine like terms when there is an x2 and x term – need to use a new formula! x = ±5

Quadratic Formula: To Solve Use the Quadratic Formula: write the equation in standard form set the function equal to 0 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” of the function) Plugging in a 0 for the y (set the equation = 0) gives x intercepts

Use Quadratic Formula to Solve: Ex. 1 y-x2 = -2x-3 1. Write in standard form y=ax2+bx+c +x2 +x2 2. Make sure function is set = 0 (This is standard form with a 0 instead of y) y = x2 -2x - 3 0 = x2 -2x - 3 a=1 b=-2 c=-3 3. Plug in a, b, c values and simplify Work continued…

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 x2+5x = 14 1. Write in standard form y=ax2+bx+c -14 -14 2. Make sure function is set = 0 (This is standard form with a 0 instead of y) x2+5x-14 = 0 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)

Clear out - in front of a by multiplying both sides by -1 Ex. 3 Solve: Clear out - in front of a by multiplying both sides by -1 0= x2+2x-5

Rationalize answer if not perfect squares

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

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

Set h=0 when rock hits ground Formula: h=-16t2+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 0=-16t2+vt+s 0=-16t2+(-30)t+1050

And

Can’t have - seconds