Quadratic Graph
Author: Bee Math Tutor
Date: 3 February 2013

Equation of line in the form y = ax² + bx + c is

The parabola crosses the y-axis at the point 

The parabola crosses the x-axis at the point(s)

and

Equation in the form y = a(x + h)² + k is

or

Solve Quadratic Equation using formula

Show line of symmetry

Show steps to rewrite formula

.................The parabola cuts the x-axis (y = 0) at two points if b² - 4ac > 0.  It will touch the x-axis at a single point if b² - 4ac =0................... ..
                                                    If b² - 4ac < 0, then the parabola will NOT touch the x-axis.

c = -3 (slider from -5 to 5, step 1)
b = 2 (slider from -5 to 5, step 0.2)
a = 1 (slider from -5 to 5, step 0.2)
J = Max((a * x^(2)) + (b * x) + c, -9, 9)
H = Min((a * x^(2)) + (b * x) + c, -9, 9)
A = (-24.986979440764244, 21.772529452229182)
B = (-9.776093661335982, 21.887024662144572)
C = (-10.507469836961032, 0.06945372984179254)
D = (-25.569829376296685, 0.01436901596344331)
poly1, a_1, b_1, c_1, d_1 = Polygon(A, B, C, D)
text3: "$ x=\frac{-(" + (LaTeX[b]) + ")±\sqrt{(" + (LaTeX[b]) + ")^2-4(" + (LaTeX[a]) + ")(" + (LaTeX[c]) + ")}}{2(" + (LaTeX[a]) + ")} $"
text5: "$ (0 ," + (LaTeX[c]) + ") $"
E: (0, c)
A1: a
B1: b
C1: c
B2: (-b)
f = Function((a * x^(2)) + (b * x) + c, -30, 30)
text1: "$ y=" + (LaTeX[f]) + " $"
F, G = Roots((a * x^(2)) + (b * x) + c, -8, 10)
text9: "$ " + (LaTeX[G]) + " $"
text7: "$ " + (LaTeX[F]) + " $"
g = CompleteSquare((a * x^(2)) + (b * x) + c)
text11: "$ y=" + (LaTeX[g]) + " $"
I = If(a > 0, H, If[a  <  0, J, ""])
text12 = If(a > 0, "The minimum point of the parabola is ", If[a  <  0, "The maximum point of the parabola is ", ""])
text13: "$ " + (LaTeX[I]) + " $"
d: (-b)
e: (b * b) - ((4 * a) * c)
h: (2 * a)
text15: "$ x=\frac{" + (LaTeX[d]) + "+\sqrt{ " + (LaTeX[e]) + " }}{" + (LaTeX[h]) + "} $"
text16: "$ x=\frac{" + (LaTeX[d]) + "-\sqrt{" + (LaTeX[e]) + "}}{" + (LaTeX[h]) + "} $"
K = (12.648830320651431, 10.63785065084748)
L = (12.72303305294454, 0.42340968779890486)
i: ((-b) + e^(0.5)) / ((2 * a))
j: ((-b) - e^(0.5)) / ((2 * a))
text18: "$ x=" + (LaTeX[i]) + " $"
text19: "$ x=" + (LaTeX[j]) + " $"
o = false
p: x = (-1 * b / ((2 * a)))
q = false
r = false
text21: "$ y=" + (LaTeX[f]) + " $"
s: b / a
t: c / a
f_1 = Function(x^(2) + (s * x) + t, -9, 9)
text22: "$ y=" + (LaTeX[a]) + "[" + (LaTeX[f_1]) + "] $"
u: (s / 2)^(2)
g_1 = Function(x^(2) + (s * x) + u - u + t, -9, 9)
text23: "$ y=" + (LaTeX[a]) + "[" + (LaTeX[g_1]) + "] $"
w: (-u) + t
v: b / ((2 * a))
h_1 = Function((x + v)^(2) + w, -9, 9)
text24: "$ y=" + (LaTeX[a]) + "[" + (LaTeX[h_1]) + "] $"
z: (a * w)
p_1 = Function((a * (x + v)^(2)) + z, -9, 9)
text25: "$ y=" + (LaTeX[p_1]) + " $"
O = (-25.023506750921406, -2.6703760098862976)
P = (-10.486849203868816, -2.608512797546572)
Q = (-10.485690765192632, -8.983093598823213)
R = (-25.069715575125226, -9.004625306623527)
poly3, o_1, p_2, q_1, r_1 = Polygon(O, P, Q, R)
S = Intersect(r_1, o_1)
T = Point(p_2)
U = Intersect(q_1, p_2)
V = Intersect(r_1, q_1)
poly4, s_1, t_1, u_1, v_1 = Polygon(S, T, U, V)
" y=" + (FormulaText[p_1]) + " ": "$ y=" + (LaTeX[p_1]) + " $"
" x=" + (FormulaText[j]) + " ": "$ x=" + (LaTeX[j]) + " $"
M = (-10.458196931948908, -2.5764087215792313)
N = (-10.504405756152726, -0.8204734018340838)
W = (-25.046208824203816, -0.8151647031847213)
Z = (-25.013976556152105, -2.5764087215792313)
poly2, m, n, w_1, z_1 = Polygon(M, N, W, Z)