Graphing Standard Form
f(x)=x^2+4x+13
Just Graph three points - Vertex and point before that and after
Should be a skinny happy face with the vertex at (-2,9)
f(x)=7x^2-14x+3
(1,-4)
g(x)=-1/3(x+2)(x+8)
DO 5 POINTS
Vertex is at (-5,3)
frowny face and fat
goes through (-2,0)
rest of points are ugly.
opens down and vertex at (-5,-2)
ugly baby t chart
4x^2-16x+9
Happy face and skinny
should have vertex (2,-7)
f(x)=3x^2+6x+5
(-1,2)
f(x)=5/9(x+9)(x+3)
opens up
vertex - (-6,-5)
goes through (-3,0)
y=2(x-4)^2+5
opens up and vertex at (4,5)
goes through (2,13)
and (5,7)
happy face with vertex at (-1,8)
f(x)=x^2-4x
(2,-4)
y=1/8(x-6)(x+2)
opens up and is fat
vertex is (2,-2)
rest of points are ugly
g(x)=-3/2(x-2)^2
opens down and vertex (2,0)
goes through (4,-6)
f(x)=4x^2+8x+9
happy face and skinny
vertex - (-1,5)
f(x)=2x^2+4x+1
(-1,-1)
y=-1/4(x-2)(x+6)
opens down and is fat
(-2,4)
goes through (0,3)
Amir stands on a balcony and throws a ball to his dog, who is at ground level.
The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by:
h(x)=-(x-2)^2+16
HINT!!! SET IT EQUAL TO 0 and then solve for x and you will get two solutions but use the one that is reasonable! (aka the positive solution)
We found that h(x)=0 for x=6 or x = -2. Since x = -2 doesn't make sense in our context, the only reasonable answer is x=6.
DAILY DOUBLE!!!!!!!!!!!!
(Cue for me to ask how much the team will wager)
square root of b^2 - 4ac
f(x)=7x^2-14x-2
(1,-9)
h(x)=-4(x-3)(x-1)
opens down and vertex at (2,4)
skinny and goes through (3,0)
The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:
m(x)=-(x-5)^2+25
find the maximum y value of the function
The number of mosquitoes is modeled by a quadratic function, whose graph is a parabola.
The maximum number of mosquitoes is reached at the vertex.
So in order to find the maximum number of mosquitoes, we need to find the vertex's y-coordinate.
The vertex of -(x-5)^2+25 is at (5,25)