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 function: h(r)= r² - 6r + 7
(r-3)² - 2
100
Solve the following equation for all values of x. x² + 9x = -14
x= -7 x= -2
100
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 Initial is our constant.
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 equation: f(r)= 2r² + 4r + 1
2(r+1)² - 1
200
Solve for x for the following function: x² + 4x -1 = 0
x= -2+√​5 x= -2−√​5
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) = –16t2 + 64t + 80, where s is in meters. What is the maximum height of the object?
144 m. The vertex of the equation is (2,144) So the maximum height is 144 meters at 2 seconds.
300
Find the vertex of f(x) = (x+6)(x+4)
(-5, -1)
300
Complete the square for the following function: h(x)= 3x² + 9x - 3
3(x+1.5)² - 9.75
300
Solve for t in the following equation: 4t​² + 8t = 4
x=−1+√​2 x=−1−√​2
300
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. At what time will the object hit the ground? (Eliminate any answer that doesn't logically fit the problem)
Set the equation equal to zero because that will show us the time when the height of the object is 0. Solve the equation. t=-2 or t= 6 Final answer: t= 6 seconds.
400
What is the vertex for f(x)= 20x² - 40x + 8
(1,-12)
400
Complete the square for the following: h(t)= -6t² + 18t + 2.5
-6(t- 1.5)² + 16
400
Solve for x in the following equation: 8x​² + 16x = 16
x=−1+√​3 x=−1−√​3
400
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) = -16t² +128t + 382. What is the maximum height of rock?
638 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: f(x)= -3.7x² + 29.6x + 5.5
-3.7(x-4)² + 64.7
500
Solve for x in the following equation. Round answers to the nearest hundredth. -3.7x​² + 29.6x = 33.3
x= 4+ √​7 or x= 4- √​7 x=6.645751 x= 1.354249 Final answer rounded to the nearest hundredth: x= 6.65 or x= 1.35
500
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) = -16t² +128t + 32. At how many seconds will the rock hit the ground? (Eliminate non-applicable answers). Round to the nearest second.
t= 8 seconds
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