The Quadratic Formula. y = ax 2 + bx + c (Standard Form) * To apply the formula, you must write the equation in standard form first! x 2 +5x = 14 (not.

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Presentation transcript:

The Quadratic Formula

y = ax 2 + bx + c (Standard Form) * To apply the formula, you must write the equation in standard form first! x 2 +5x = 14 (not in standard form) -14 x 2 +5x-14 = 0 (This is standard form.) This gives us the x-intercepts

Quadratic Equation:

x = 2,-7 x 2 +5x-14 = 0

To graph, find the vertex Plug back in for y.

Change -14 to ¼’s Y value is

Vertex is To graph, make mixed numbers y x -7 2

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

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

AND Use calculator to find exact ≈1.45

Find Vertex and Graph Vertex (-1,6)

x y Why does it open down? The original was a negative!

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

Formula: h=-16t 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 0=-16t 2 +vt+s 0=-16t 2 +(-30)t+1050

And

Can’t have - seconds