f(x)=a \left ( x+b \right)^2+c

Completing the Square

Reveal Answer

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a = Random(1, 5)
b = Random(-10, 10)
c = Random(-15, 15)
f(x) = (a * x^(2)) + (b * x) + c
d: b / ((2 * a))
e: (((-a) * d) * d) + c
text2 = FractionText(d)
text3 = FractionText(e)
text6: "f(x)=" + (LaTeX[f]) + ""
text7 = If(d < 0, "-", "+")
text8 = If(e < 0, "-", "+")
g = If(d < 0, (-d), d)
text9 = FractionText(g)
h = If(e < 0, (-e), e)
text10 = FractionText(h)
text1: "f(x)=" + (LaTeX[a]) + "\left ( x" + (LaTeX[text7]) + "" + (LaTeX[text9]) + "\right)^2" + (LaTeX[text8]) + "" + (LaTeX[text10]) + ""
a_2 = Random(-5, -1)
b_2 = Random(-10, 10)
c_2 = Random(-15, 15)
d_2: b_2 / ((2 * a_2))
e_2: (((-a_2) * d_2) * d_2) + c_2
i = If(d_2 < 0, (-d_2), d_2)
j = If(e_2 < 0, (-e_2), e_2)
p(x) = (a_2 * x^(2)) + (b_2 * x) + c_2
text11: "p(x)=" + (LaTeX[p]) + ""
text12 = FractionText(d_2)
text13 = FractionText(e_2)
text14 = If(d_2 < 0, "-", "+")
text15 = If(e_2 < 0, "-", "+")
text16 = FractionText(i)
text17 = FractionText(j)
text18: "p(x)=" + (LaTeX[a_2]) + " \left ( x" + (LaTeX[text14]) + "" + (LaTeX[text16]) + "\right)^2" + (LaTeX[text15]) + "" + (LaTeX[text17]) + ""
k: false