Directrix and Focus
Finding roots
Changing to VF or SF
Word Problems
Misc.
100
Find the 'a' value of the parabola from the information below.
Focus: (4,0)
Directrix: y=-4
a = -0.75
100
What is the quadratic equation?
Time: 10 seconds
Calculator: No
(-b ∓ √b^2-4ac)/2a
100
Time limit: 1 minute
x^2 + 2x + 1
y = (x + 1)^ 2
100
Jimmy just came from math. He learned about the focus and directrix. As he is walking home, he sees a smiley face. He graphs it on a coordinate plane. The axis of symmetry is along -6 and the y-coordinate of the vertex is 2.5. He also finds that that “a” is 0.35. FInd the focus and Directrix. You have 2 minutes.
Focus: -6,3.9
Directrix: 1.1
100
What happens when you change the h, k and a, values in a parabola?
Time Limit: 1 ½ minutes
h= parabola moves side to side, k= parabola moves up and down, a= the width of the parabola (the smaller the number, the wider the parabola, if a <0, the parabola is flipped)
200
Find the focus and the directrix:
y-3=-(x+2)^2
Time Limit: 1 minute
Focus: (-2, .75) Directrix: y=1 ¼
200
Find the roots for the equation: 3x^2 + 2x - 12
Time: 3 minutes and 15 seconds
Calculator: Yes
1.69 , 2.36
200
Convert this equation into vertex form.
y = x^2
Time limit: 30 seconds
y = x^2
200
A person is skydiving from a plane. The person inside is at 12,000 feet. They jump out, and after 5 seconds they have dropped 4,000 feet. Find out when they reach the bottom, and give us the equation in vertex form. Round to the nearest whole number. You have 1 minute and 45 seconds.
A=-320(x^2)+12,000=y
About 6.
200
What are the roots of:
y=2(x-3)² +5
Time limit: 1 minute
Roots are not real
300
Find focus and directrix given the following equation:
y=(x-6)^2+2
Time Limit: 1 minute and 30 seconds
Focus (-6, 2.25) Directrix y=1.75
300
Find the roots of the equation y=2(x-1)^2 +3
Time 5 mins
Calculator: Yes
No real roots
300
Time limit: 2 minutes
Y = -¼(x+9)^2 - 5
y=-1/4x^2 - 4.5x - 25¼
300
A person walked into a nail salon to get a french manicure. They had long, almond shaped nails. The formula for them is y = -5x^2+2x+6. Find the roots and vertex. You do not have to graph it, calculators are allowed. You have 2 minutes.
Roots - x= -0.914 // x= 1.314
Vertex - (0.2, 6.2)
300
Change: y=4(x+5)²-10.5 into standard form
Time Limit: 1 ¼ minutes
4x^2+40x+89.5=y
400
Find the focus and directrix:
y=34(x+90)^2+5
(90,2) Directrix: y=2 (rounded)
400
Find the roots directrix y=4.9 focus= 0,4.5
Time 7 minutes
Calculator: Yes
-1.18 and 1.18 = x
400
Given the vertex and a point on the parabola, find the equations for the parabola in both standard and vertex form.
Time Limit: 4 minutes
Standard Form: y=3x^2+10x+6
Vertex Form: y=3(x+5/3)^2-2 ⅓
400
Two people are throwing a ball across a 16 feet wide field. Where there hands are is the point of origin. When the ball is thrown, it makes a parabolic shape, and the point where it’s highest is (8,10), the vertex. The equation of the parabola is y= -0.156 (x-8)^2+10. Find the focus, directrix, roots, and graph the parabola. You have 3 minutes.
A= Roots: (0,0) and (16,0)
Directrix: 11.603 Focus: 8.397
400
Write an equation for a parabola with a focus at: (7,14), and a directrix at: y=106 and find the roots
Time Limit: 3 Minutes
1/184(x-7)^2+60
Roots: (-85, 106) (99, 106)
y=-2(x-100\right)^2+300
500
Find the focus and directrix of this equation:
y=495(x+68)^2-64
Time Limit: 2 minutes and 30 seconds
(68, -63.99949) Directrix: y=-64.00050
500
Prove the Vertex formula on the whiteboard, -b/2a using the midpoint, midpoint formula (x1+x2)/2, and the quadratic formula.
500
Given a focus of (2, 1) and a directrix of y = -3, write the equation for the parabola in standard form.
Time limit: 2 minutes
Ans: y = 1/8x^2 - 1/2x - ½
500
A person is walking through the forest. They see a tiger 18 feet away. The tiger leaps and it’s highest point is 10 feet tall, while it is 5 feet away from the person, Luckily for the person, the tiger lands 13 feet behind them, so they have time to run away. Write the equation in V.F and S.F. Assume the person is at the point of origin. You have 3 minutes and 15 seconds
-0.06(x-5)^2+10=y
-x^2/0.06 +10x/0.06 +1.5=y
500
Zarta and Amnber are business partners and are creating a startup. This equation represents how much money they earn in any, or y, month:
-2x²+400x-19700=y
When will their company reach the maximum amount of earnings and at which month. Once you have found the max amount, put the parabola into vertex form.
Time Limit: 3 minutes
(100, 300)
month 100