(x - S)² = R²

x = S \pm R

Show R

Show formulae

Show symmetry

Show roots

q = 5 (slider from -4 to 8, step 0.2)
p = 6 (slider from -8 to 8, step 0.2)
r2: (p / 2)^(2) - q
a = 1 (slider from -5 to 5, step 0.1)
f(x) = x^(2) + p * x + q
S: ((-p) / (2 * a), 0)
d = OrthogonalLine(S, xAxis)
Q = Intersect(f, yAxis)
x_1, x_2 = Intersect(f, xAxis)
s: (-p) / (2 * a)
Vertex = Extremum(f)
text2: "x² + " + p + "x + " + q + " = 0"
text3: "x² + " + p + "x = - " + q
text4: "x² + 2(" + p + "/2)x + (" + p + "/2)² = (" + p + "/2)² - " + q
text5: "(x + " + (p / 2) + ")² = " + (p / 2) + "² - " + q
text6: "(x + " + (p / 2) + ")² = " + (p / 2) + "² - " + q + " = " + r2 + ""
text7: "(x + " + (p / 2) + ") = " + "\pm\sqrt{" + r2 + "}"
text8: "R² = " + r2
text9: "R = \sqrt{ " + r2 + " }"
b = Segment(S, x_2)
c = Segment(S, Vertex)
text10: "x = -" + (p / 2) + "\pm\sqrt{" + r2 + "}"
e = true
g = true
h = true
i = true
text1: "Line of symmetry: x = " + s + ""