Solving by factoring
Finding zeros
Quadratic formula
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(Solve by taking square roots or vertex to standard form or finding zeros.)
(Solve by taking square roots or vertex to standard form or finding zeros.)
Hmmm??
100
Solve this quadratics by factoring.
x2 + 2x = 3
x2 + 2x - 3 = 0
= (x-1)(x+3) = 0
x = 1 or x = 3
100
Which of the following answers are the zeros of this equation?
2x2 -5x - 12 = 0
A. (-1,-2) and (-3.5, 2)
B. (0, -12)
C. (1.25, -15.125)
D. 4 and -3/2
D. 4 and -3/2
100
Is this quadratic formula?
Yes
100
Solve this equation by taking square roots.
x2 + 1 = 26
x2 = 25
x= 5, -5
100
Graph y = 2x^2 -3x +7
See board
200
Solve this quadratic equation by factoring.
X2 + 16 = 10x
x2 - 10x + 16 =0
(x-2)(x-8)
x = 2 or x = 8
200
What are the zeros also known as
x intercepts. roots, solutions.
200
Are these steps right?
Step 1. Identify a, b, and c and plug them into the quadratic formula.
Step 2. Use the order of operations to simplify the quadratic formula.
Step 3. Find the positive answer only.
No - both answers work. (Negative answers are OK too)
200
Write this equation in standard form.
(x-4)2 - 16 = 0
x2-8x+16
200
When will a quadratic inequality have a solid parabola?
When it is <= or >=
300
Solve this quadratics equation by factoring.
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
300
Solve the quadratic equation using the quadratic formula.
3x2 + 7x + 4 = 0
x = -4/3
x = -1
300
Solve x2 - 8x + 14 = 0 using the quadratic formula.
x = -(-8) ±√ (-8)2 - 4(1)(14) / 2(1)
= 8 ±√ 8 / 2
= 5.41 and 2.59
300
The points of a graph are shown below. What are the solutions of the function. Solutions are also known as?
(0,3)(1,5)
(4,2)
(5, 0)
(7, 9)
(0,8)
(12,0)
(12,0) and (5,0)
The y-value is always ZERO at the x-intercept
remember a point is (x,y)
300
When will a quadratic inequality have a dashed parabola? greater than or equal to? greater than? less than or equal to? less than? This is from Unit 2
When it is strictly > or <
400
What's the first step to solve quadratics by factoring
Step 1. Write the equation in standard form.
400
Which equation has solutions x= -3 and x= -1
A. x2 - 3x - 1 = 0
B. 3x2 - x + 1 = 0
C. x2 + 4x + 3 = 0
D. x2 + 6x + 12= 0
C. x2 + 4x + 3
box method (area model)
400
Solve x2 + 4x - 21 = 0 by using quadratic formula.
x = 3 or -7
400
What do you have to do first to solve quadratics equation by taking square roots?
Isolate the square. Get x by itself
400
Write the following in standard form:
y = 3(x - 4)2 +8
3x2-24x+56
500
Miss Gurl uses factoring to find the zeros of the equation x2 + 15x - 32 = y. She concludes that the graph intersects the x - axis at x = 17 and x = -2. Is Beyonce correct or incorrect? If she is incorrect, choose the statement that correctly completes the statement.
A. She is correct.
B. She in incorrect because x2 + 15x - 32 = y is equivalent to (x + 17)(x - 2)
C. She in incorrect because x2 + 15x - 32 = y is equivalent to (x - 17)(x + 2)
D. She in incorrect because x2 + 15x - 32 = y is equivalent to (x + 17)(x + 2)
E. She in incorrect because x2 + 15x - 32 = y is equivalent to (x - 17)(x - 2)
B. She in incorrect because x2 + 15x - 32 = y is equivalent to (x + 17)(x - 2)
The x-intercepts are x = -17 and x = 2. WATCH YOUR SIGNS!!!!!!!!!
500
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
500
Solve 2x2 = 7x + 6 by using quadratic formula.
x = -(-7) ±√(-7)2 -4(2)(-6) / 2(2)
x = (7 ±√ 97) / 4
x =4.21 and -.71
500
Solve by taking the square root of:
x2 + 1 = 325
x = plus OR minus 18
500
Write the following in standard form:
f(x) = -3(x -4)(x - 6)
REMEMBER TO CHECK YOUR ANSWER IS DESMOS. GRAPHS SHOULD BE RIGHT ON TOP OF EACH OTHER LIKE TWO PIECES OF BREAD
y = -3x2 + 30x - 72