Completing the Square
Rewrite a quadratic in vertex form.
ax² + bx + c = a(x − h)² + k
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Solve equations, work with quadratics, factor expressions, and explore functions and proportions.
Rewrite a quadratic in vertex form.
ax² + bx + c = a(x − h)² + k
Open calculatorFind a variation constant or an unknown.
Direct: y = kx; inverse: y = k/x
Open calculatorClassify the roots of a quadratic.
D = b² − 4ac
Open calculatorSolve a linear equation with fractional coefficients.
(ax + b) / m = (cx + d) / n
Open calculatorFind real or complex quadratic roots.
x = (−b ± √(b² − 4ac)) / 2a
Open calculatorFind the vertex of a parabola.
h = −b / 2a; k = f(h)
Open calculatorFind b from a line or point and slope.
Ax + By + C = 0; y-intercept = −C / B
Open calculatorExpand a binomial with Pascal coefficients.
(a + b)ⁿ = Σ C(n,k)aⁿ⁻ᵏbᵏ
Open calculatorSafely substitute into an algebraic function.
f(x) → f(value)
Open calculatorSolve one unknown in a/b = c/d.
a / b = c / d ⇒ ad = bc
Open calculatorClassify and solve a 2×2 system.
ax + by = c; dx + ey = f
Open calculatorSolve a 2×2 system by determinants.
x = Dₓ / D; y = Dᵧ / D
Open calculatorSolve linear and quadratic polynomial equations.
ax² + bx + c = 0
Open calculatorFactor integer quadratic expressions.
ax² + bx + c = a(x − r₁)(x − r₂)
Open calculatorConvert line equation forms.
y − y₁ = m(x − x₁)
Open calculatorGaussian elimination for a 3×3 system.
[A | b] → RREF([A | b])
Open calculatorEvaluate the current function at x=0.
y-intercept = (0, f(0))
Open calculatorFit y=ax²+bx+c through three points.
y = ax² + bx + c
Open calculatorBoundary style and shading guidance.
Ax + By ≶ C
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