Form Frenzy 🌀
What is vertex form?
What is standard form?
y=a(x−h)2+k
y=ax2+bx+c
Solve the factored equation below: (x-1)(x+9)
x=1, -9
Solve: x2 = 16
x=4,−4
Simplify i23
-i
The discriminant discriminates to tell ______ and ______ of solutions possible.
Given the quadratic y=−12(x−4)2 +3, find the vertex and determine if it opens upward or downward.
Opens: Downward
Vertex: (4,3)
Factor: 3x2 - 12x + 12
3(x−2)2
Solve the following: (x+3)2 = 36
x=3,-9
Simplify (7-3i)-(-2+6i)
9−9i
The discriminant of f(x)=5x2+27x+10 is ________.
Δ=529
Write the quadratic function in vertex form (Hint: complete the square or use -B/2A): f(x)=x2-2x-8
f(x)=(x−1)2−9
Solve by factoring:
f(x)=6x2+x-4=11
x=3/2, -5/3
Factor 16x2−25
x=(4x−5)(4x+5)
Evaluate Expression: √-8√-392
−56
Use the discriminant to determine the types of solutions then solve using the quadratic formula:x2+2=-3x
Δ=1, the quadratic has two distinct real rational solutions.
x=-1,-2
The vertex of a parabola is (h,k) = (-3, 18). The parabola also goes through the point (x, y) =( 0,0). Write the equation of the parabola.
y=−2(x+3)2+18
Solve the following equations:
1. 10x2−25x=0
2. 3x2=27
3. x2-25=0
1. x=0,5/2
2. x=3,-3
3. x=5,-5
Solve for x: 4+2(x−1)2=8
x=1± √2
Simplify (3+2i)(4−5i)
22-7i
Solve the following using the quadratic formula: f(x)=2x2+5x−7=0
x=1, -7/2
Write the equation y = 16(x-1)2 +20 in the form y = ax2 + bx + c.
y=16x2−32x+36
Write the equation for a parabola with x-intercepts -3 and 1 that passes through (1, -8). HINT: Consider the factored form could look like: y = a (x-a) (x-b)
y=2(x+1)(x−3)
TRUE or FALSE?
All polynomials of the form a2+b2 can be factored using the difference of squares formula.
False ✅ Explanation: The difference of squares only works for a2−b2. Sums of squares are not factorable over the reals.
Simplify: 6+5i/1-6i
-24/37 + 41/37i
Solve the quadratic equation using the quadratic formula: f(x)=3x2−2x−8
x=2, -4/3