Transformations of Quadratic Functions
Describe how the graph of the function g(x) = x2+3 is related to the graph of the parent function f(x) = x2
What is translated up 3 units?
Factor x2-6x+9
What is (x-3)2?
Solve the equation x2+3x-4=0 using the Quadratic formula. Round to the nearest tenth if necessary.
What is 1.1 and -4.1?
State the value of the discriminant of the equation x2+2x-3. Then determine the amount of solutions it has.
What is that the discriminant is 16, which means there is two real solutions?
Two numbers have a sum of 3 and a product of -18. The quadratic equation -n2+3n+18=0 can be used to determine the two numbers. Graph the functions f(n)=-n2+3n+18 and determine its x-intercepts. Then determine the two numbers.
What is the x-intercepts are 6 and -3, so the solutions are 6 and -3.
Describe how the graph of the function g(x) = -2x2-3/4 is related to the graph of the parent function f(x) = x2
What is reflected over the x-axis, stretched vertically, and translated down 3/4 of a unit?
Factor x2-6x-91
What is (x+7) (x-13)?
Solve the equation 2x2-5x-9=0 using the Quadratic formula. Round to the nearest tenth if necessary.
What is 3.7 and -1.2?
State the value of the discriminant for the equation -x2+4x+4. Then determine the amount of solutions it has.
What is that the discriminant is 0, which means that there is one real solution?
Ted popped a baseball straight u with an original upward velocity of 48 feet per second. the height, h, in feet, of the ball above the ground is measured h(t)=-16t2+48+3. How long was the ball in the air if the catcher catches in three feet in the above the ground?
What is 6.175 seconds?
Consider the functions f(x) = (x+2)2-3 and g(x) = (x-4)2+5. Describe the transformation from f(x) to g(x).
What is translated to the right 6 units and translated up 8 units?
Factor 2x2+13x+15
What is (2x+3) (x+5)?
Solve the equation x2+3x+8=0 using the Quadratic formula. Round to the nearest tenth if necessary.
What is no solution?
State the value of the discriminant for the equation 2x2+4x+5. Then determine the amount of solutions it has.
What is that the discriminant is equal to -24, which means there are no real solutions.
Aiden owns a business laying bricks on skyscrapers. The function x2+30x+1100 models the profit, y, that Aiden made in month y for the first year in his business. In which month does Aiden's profit reach $2000?
What is month 20?
Consider the functions f(x)= -4x2+1, g(x)= 1/2x2-2, h(x)= x2-4, i(x)= -2x2+3. List the functions from highest point of the vertex to the lowest point of the vertex
What is i(x)= -2x2+3, f(x)= -4x2+1, g(x)= 1/2x2-2, h(x)= x2-4?
Factor 6x2-13x+6
What is (3x-2) (2x-3)?
Solve the equation 3x2+4x-6=0 using the Quadratic formula. Round to the nearest tenth if necessary.
What is 0.9 and -2.2?
State the value of the discriminant for the equation 3x2+5x-2. Then determine the amount of solutions it has.
What is that the discriminant is equal to 49, which means there are two real solutions?
A roller coaster is suspended with steel supports. The function f(x)=x2+200 represents the height in feet of the steel supports of the roller coaster where x=0 represents the midpoint of the ride what is the length of roller coaster when the supports intersect the ride?
What is 51 feet?
Describe how the graph of the function g(x)=-(2-x)2+1 is related to the graph of the parent function f(x)=x2
What is reflected of the x-axis, reflected over the y-axis, translated left 2 units, and translated up 1 unit?
Consider the trinomial 4x2+12x+k. What number can you replace with the variable k to make a perfect square trinomial?
What is 9?
Solve the equation -2x2+5x-7=0 using the Quadratic formula. Round to the nearest tenth if necessary.
What is no solution?
State the value of the discriminant for the equation 4x2-8x-4. Then determine the amount of solutions it has.
What is that the discriminant is equal to 0, which means that there is one real solution?
Robert dropped a tennis ball off a 169-foot cliff. The height, h, of the tennis ball t seconds after Robert drops it is represented by the equation h=-16t2+26t+169. To the nearest tenth of a seconds, how long does the tennis ball take to reach the ground?
What is 4.3 seconds?