Factoring
Factor: x2+7x+10
(x+2)(x+5)
What is the vertex form of a quadratic?
What determines if the graph opens up or down?
f(x) = a(x - h)2 + k
Opens up when a is positive, opens down when a is negative.
What is the standard form equation of a quadratic? AND How do you solve for the vertex using the standard form?
Standard form: y=ax²+bx+c
Vertex: x=-b/(2a), plug x in to solve for y.
The diameter of a circle is 6 cm. What is the area and circumference of the circle?
Area: 9π
Circumference: 6π
What do you do to the b value to correctly complete the square?
divide it by 2 and square the result
Factor: 8x3 - 18x
2x(2x+3)(2x-3)
Does the graph of this equation open up or down?
f(x) = -(x + 3)2 - 5
What is the axis of symmetry?
Opens down. AOS: x=-3
What is the vertex of the quadratic function:
y = x2 - 6x + 11?
(3,2)
What is the center and radius of this circle?
(x - 5)2 + (y + 2)2 = 49
Center: (5, -2)
Radius = 7
When factoring x2 - 4x + 4 = 20, what goes in the blank? (x - __ )2 = 20
2
Factor: 3x3-x2+6x-2
(x2+2)(3x-1)
Find the domain AND range of the function
y = -2(x + 4)2 + 7
Domain: (-∞,∞)
Range: (-∞, 7]
Convert the equation y= x2-2x-5 into vertex form
y= (x-1)2-6
Write the equation of a circle with a center at (-2,0) with a diameter of 8. Graph the circle.
(x+2)2+y2=16
Change the following equation to standard form
x2+y2-4x+12y-8=0
(x-2)2+(y+6)2=48
Factor: 3x2+11x+10
(3x+5)(x+2)
Find the y-intercepts of the function
y = -3(x + 2)2 - 5. Graph the function.
Y-intercept: (0, -17)
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t2 + 64t + 80.
What will be the object's maximum height?
144 feet
Write an equation of a circle with center (-2,5) and point (2,5).
(x+2)2+(y-5)2=16
What is the center for the circle with this equation x²+y²+4x+6y-36=0?
Center: (-2,-3)
Solve: 2x2 - 9x - 35 = 0
x= -5/2, x=7
Find the y-intercept and x-interecept(s) of the quadratic y = (x + 3)2 - 7
x-intercepts:(-0.4, 0) and (-5.6, 0)
y-intercept: (0,2)
How fast would you reach the water if you jump of a cliff using the formula: h(t) = -16t2 + 8t + 24?
1.5 seconds
Write the equation of a circle given that points (-2,-15) and (6,5) are the endpoints of a diameter.
(x-2)2+(y+5)2=116
Determine the equation of the circle in standard form: 2x² + 2y² + 8x + 12y - 72 = 0. Solve for area and circumference.
(x+2)2 + (y+3)2 = 49
Area: 49∏ Circumference: 14∏