Find the Vertex
Complete the Square
Solve the Quadratic Function
Dissecting Word Problems
100
What is the vertex for the following function written in vertex form? f(x) = 4(x-3)² + 8
(3,8)
100
Complete the square for the following: f(x)= x² + 2x + 3
(x+1)² + 2
100
Solve for all values of x: 2(x + 8)(x - 5) = 0
x= -8 x= 5
100
A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d(t) = -t² – 4t + 382. What is the initial height of the rock?
382 feet.
200
What is the vertex for the following function written in vertex form? g(x) = -3(x+2)² - 9
(-2, -9)
200
Complete the square for the following function: g(x) = x² + 4x + 8
(x+2)² + 4
200
Solve the following equation for all values of x. x² + 9x + 14 = 0
x= -7 x= -2
200
An object is launched in the air. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t² + 19.6t + 58.8, where s is in meters. What is the initial height the object is launched at?
58.8 meters
300
Find the vertex of f(x) = (x+6)(x+4)
(-5, -1)
300
Complete the square for the following function: h(r)= r² - 6r + 7
(r-3)² - 2
300
Solve the following equation for all values of x: x² - 17x = - 72
x=8 x= 9
300
A diver is in the water and goes deeper to retrieve an item and then go back to the surface. The function of her height in the water h at time t seconds is h(t)= t² - 2t - 3. At what time will she reach ground level? (hint: height will be 0) Eliminate illogical answer.
3 seconds.
400
What is the vertex for f(x)= 20x² - 40x + 8
(1,-12)
400
Complete the square for the following function: f(t) = t² - 20t - 2
(t-10)² - 102
400
Solve for x for the following function: x² + 4x -1 = 0
x= -2+√​5 x= -2−√​5
400
A diver is in the water and goes deeper to retrieve an item and then go back to the surface. The function of her height in the water h at time t seconds is h(t)= t² - 2t - 3. What is her minimum height in the water?
-4 feet
500
John says the vertex for f(x)= x² - 6x - 13 is (-3, -13). Is he correct? If he is wrong, what is the correct vertex for this function?
No, the correct vertex is (3,-22) because vertex form of a quadratic function is f(x)= a(x-h)² + k. Since (h, k) is our vertex it would be f(x) =(x-3)² - 22. So (h, k) would be (3,-22)
500
Complete the square for the following function: g(h)= h² - 100h + 100
(h-50)² - 2400
500
Solve for x in the following equation: x​² + 6x = 2
x=−3+√​11 x=−3−√​11 ​ ​​
500
A diver is in the water and goes deeper to retrieve an item and then go back to the surface. The function of her height in the water h at time t seconds is h(t)= t² - 16t - 7. At what time will she reach her minimum height?
8 seconds.
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