Coefficients and Vertex
The coefficient of the quatratic term in 5x^2 + 8x + 3.
Since the quadratic term is x^2, and the coefficient is the number before that, what is 5?
This is what is in the radical of the quadratic formula for f(x) = 4x^2+7-5
What is b^2-4ac = (7)^2 - 4(4)(-5) = 49+80 = 129?
This is the function if f(x) = x^2 + 2x + 3 is shifted to the right by 3
Since f(x-k) shifts a graph to the right by k units, we sub x-3 in for all values of x, so what is g(x) = (x-3)^2 + 2(x-3) + 3 = x^2 -6x +9 +2x - 6 + 3 = x^2 -4x + 6 ?
The vertex form of the standard quatratic equation f(x) = x^2 + 10x + 10
What is f(x) = (x + 5)^2 - 15?
This is what is in the radical of the quadratic formula for f(x) = 3x^2-7+5
What is b^2-4ac = (-7)^2 - 4(3)(5) = 49-60 =-11?
This is the function if f(x) = x^2 + 2x + 3 is shifted to the left by 3
Since f(x+k) shifts a graph to the left by k units, we sub x+3 in for all values of x, so what is g(x) = (x+3)^2 + 2(x+3) + 3 = x^2 +6x +9 +2x + 6 + 3 = x^2 +8x + 12 ?
The formula for the axis of symmetry of the parabola 3x^2 + 9x + 2
What is f(x) = -b/2a = -9/2(3) = -3/2
This is how many real solutions there are for the equation 0 = 5x^2+7-6
Since b^2-4ac = (7)^2 - 4(5)(-6) = 49+120 = 169 is a positive number, there are two real solutions to the equation. What is two?
This is the function if f(x) = x^2 + 2x + 3 is shifted up by 3
Since f(x) + k shifts the function up by k unit, what is g(x) = x^2 +2x +3 +3 = x^2 + 2x + 6?
The axis of symmetry crosses the parabolic function f(x) = x^2 - 4x +7 at this point.
Putting this into vertex form f(x) = (x-2)^2 +3 where h=2 and k=3, so the vertex is (2,3). What is (2,3)?
This is how many real solutions there are for the equation 0 = 5x^2+7+6
Since b^2-4ac = (7)^2 - 4(5)(6) = 49-120 = -71 is a negative number, there are no real solutions to the equation. What is none?
Using the sum of cubes pattern, this is the solution of 8^3 + 2^3
Since a^3 + b^3 = (a + b)(a^2 − ab + b^2),if a is 8 and b is 2, we have (8+2)(8^2 - 8*2 +2^2) = 10(64-16+4) = 10(52) = 520 . What is 520?
This is the coordinate of the vertex of a quadratic function f(x) = −4(x − 3)^2 + 5
Since this is in vertex form a(x-h)^2+k where (h,k) is the vertex, what is (3,5)?
This is how many real solutions there are for the equation 0 = x^2+4+4
Since b^2-4ac = (4)^2 - 4(1)(4) = 16-16 = 0, there is one real solution to the equation. What is one?
These are the values of x for 0 = 2x^2 -3x -7
Using the quadratic formula x=(−b±sqrt(b2−4ac))/2a, what is (3±sqrt((-32-4(2)(-7))/(2(2)) = (3±sqrt(9+56))/4 = (3±sqrt(65))/4 so x=3/4 + sqrt(65)/4 and x=3/4 - sqrt(65)/4 ?