Vertex and Vertex Form
How do we find our vertex?
h= -b/2a
f(x) = -2(x-1)2+4
-2x2+4x+2
If the graph has a negative a-value then it _ _ _ _ _ _ _ _ _ _ _ _.
concaves down
A phone app is launched. The equation A(m) = -0.22m2 + 2.5m + 4.1 gives the number of new app users (in millions) after m months since the launch. How many app users were there at the initial launch?
4.1 million users
x2-9x + 20
x = 4, x = 5
f(x) = 3x2 - 12x + 4
What is our vertex? What is the equation in vertex form?
(2,-8) y= 3(x-2)2 - 8
f(x) = 3(x+2)2-5
3x2+12x+7
What is the domain and range?
(-inf, inf) (-inf, 0]
Suppose a pumpkin is shot into the air with a cannon. After t seconds, the height (in feet) of the pumpkin can be represented by the following function, W(t) = -1.3t2 + 26t + 4. How long does it take the pumpkin to reach its maximum height?
10 seconds
2x2 - 5x - 3
x = -1/2 x = 3
F(x) = 3(x+2)2 - 5
What is the vertex?
(-2, -5)
f(x) = -2(x+3)2 + 27
-2x2-12x + 9
a = 3
A ball is thrown in the air from the top of a building. Its height, in meters above the ground, as a function of time in seconds is given by h(t) = -4.9t2 + 24t + 8. What is the maximum height the ball reaches?
37.4 meters
x2 - 8x + 16
x = 4
When the graph concaves up, the vertex is a _ _ _ _ _ _ _
minimum
f(x) = -1(x+2)2 + 11
-x2 - 4x + 7
What are the intervals of increase and decrease?
Increase: (-inf, 1) Decrease: (1, inf)
A golf ball is hit so that its height h in feet after t seconds is given by h(t) = -15t2 + 60t. Determine the height of the ball at 1.5 seconds.
56.25 ft
2x2 + 6x - 36
x = -6 x = 3
The vertex is also known as a _ _ _ _ _ _ _ _ _ _ _ _.
turning point.
When converting from vertex to standard form, the first step is what?
Exponent; Squaring parenthesis
What is the a-value of the quadratic?
a = 1/2
A phone app is launched. The equation A(m) = -0.22m2 + 2.5m + 4.1 gives the number of new app users (in millions) after m months since the launch. What is the maximum number of new app users reached?
11.2 million users
x3 - 4x2 - 12x
x = 0, x =6, x = -2