Graphing
After finding the vertex, what must you do next to graph a quadratic equation?
Find two "random" points
What is factoring?
To break up a number into other, smaller, numbers that can multiply together to create the original number.
What is Completing The Square?
"A method of solving quadratic equations; completing the square turns every quadratic equation into the form x2 = c" - Gradpoint
What is the Vertical Motion formula?
h = -16t2 + vt + c
What is the Quadratic Equation?
ax2 + bx + c = 0
What does it mean when for a formula when a parabola opens downwards?
If "a>0" then the parabola opens up, if "a<0" then the parabola opens downwards
x2 – 13x = 30
x = -2
or
x = 15
What "thingy thing whatever whatcha macallit thing" is used to solve Completing The Square problems?
(-b/2)2
If a rock is dropped off of a bridge that is 30 feet above a river, how long will it take the rock to hit the water?
h = -16t2 + 30
t = 1.369
3x2 + 7 = 55
x = 4
x = -4
y = x2 + 2x - 8
Find the vertex
(-1, -9)
27x2 = 12
x = -2/3
or
x = 2/3
x2 – 8x + 5 = 0
x = 4 plus minus the square root of 11
A tennis player hits a ball 1 meter above the ground with a velocity of 20 m/sec. When will the ball be at a height of 1 meter again?
1 = -4.9t2 + 20t + 1
t = 4.1 sec
x2 – 4x – 8 = 0
x = 5/3
x = -5
y = -3x2 + 3
Find the vertex
(0,3)
20x2 – 130x = –200
x = 5/2
or
x = 4
4x2 + 8x – 9 = 0
x = -1 plus minus the square root of 13 divided by 2
A tennis player hits a ball 1 meter above the ground with a velocity of 20 m/sec. How long will it take the ball to hit the ground?
0 = -4.9t2 + 20t + 1
t = 4.13
3x2 + 10 - 25 = 0
x = 2 plus minus 2 times the square root of 3
y = x2 + 4x + 7
(-2, 3)
27x2 = 12
x = 4
or
x = 12
5x2 +20x +32 = 0
x = -2 plus minus 2 times the square root of 15 divided by 5
A hawk, flying at a height of 50 feet, spots a rat on the ground. If he dives down to catch the rat at a speed of 45 feet per second, how long will it take him to catch the rat?
0 = -16t2 - 45t + 50
t = 0.9
4x2 + 3x – 2 = 0
x = -3 plus minus the square root of 41 divided by 8