Solving by factoring
What's the first step to solve quadratics by factoring
Step 1. Write the equation in standard form.
What's the first thing you have to do to complete the square?
Make sure that it is written in standard form and = to 0
ax2 + bx + c =0
(Remember, when y is 0 you will find the x-intercepts) (x,0)
What do you have to do first to solve quadratics equation by taking square roots?
Isolate the square.
How is standard form written for a quadratic equation?
y = ax2 + bx + c
or
ax2 + bx + c = 0
What do you have to do after you write the equation in the standard form?
Step 2. Factor completely.
Step 3. Use the zero product property.
Step 4. Solve each factor to get the x.
Solve y = x2 − 6x by completing the square.
x2 − 6x = 0
x2 − 6x + 9 = 0 + 9
(x -3)2 = 9
sqrt(x -3)^2 = sqrt9
x-3 = +- 3
x = 0
x = 6
Solve this equation by taking square roots.
x2 + 1 = 37
x2 = 36
x= 6, -6
How is vertex form written for a Quadratic Equation?
y = a(x-h)2 + k
or
a(x-h)2 + k = 0
Solve this quadratics by factoring to find the x-intercepts. (Hint: box method from unit 7 notes)
x2 + 2x = 3
x2 + 2x - 3 = 0
(x-1)(x+3) = 0
x = 1 or x = -3
Solve y = x2 − 25 by completing the square.
x2 − 25 = 0
x2 = 25
(x)2 = 25
sqrt(x)^2 = sqrt25
x= +- 25
x = 5
x = -5
Solve this equation by taking square roots.
x2 - 10 = 54
x2 = 64
x = 8 , -8
What is the formula for x-vertex coordinate when the quadratic equation is in standard form?
x =- b/(2a)
Solve this quadratics by factoring to find the x-intercepts. (Hint: box method from unit 7 notes)
X2 + 16 = 10x
x2 - 10x + 16 =0
(x-2)(x-8)
x = 2 or x = 8
Solve x2 − 6x − 3 = 0 by completing the square.
x2−6x=3
x2−6x+(−3)2=3+9
(x−3)2=12
x−3=±√12
x=6.46 and -.46
Solve this equation by taking square roots.
(x-4)2 - 16 = 0
(x-4)2 = 16
x- 4 =± 4
x = 0 or 8
What is the formula for the vertex when the quadratic equation is in vertex form?
(-h, k)
Solve this quadratics by factoring to find the x-intercepts. (Hint: box method from unit 7 notes)
18x2 - 3x = 6
18x2 - 3x -6 = 0
= 3(6x2 - x - 2) = 0
= 3(3x -2)(2x +1)= 0
= 3x -2 = 0 2x + 1 = 0
x = 2/3 or x -1/2
Solve x2 - 6x + 7 = 0
x2 - 6x = -7
x2 -6x + (3)2 = -7 + 9
x2 -6x + 9 = 2
(x-3)2 = 2
x -3 = ± √2
x = 4.42 and 1.59
Solve this equation by taking square roots.
(x+7)2 - 11 = 0
(x+7)2 = 11
x + 7 = ±√11
x = -3.68 and -10.32
("a value"uarr or darr)/(1harr)