Pre-Calculus Equation Calculator

ax² — Quadratic

Roots, discriminant, vertex, Vieta

p(x) — Polynomial Roots

Bisection on [−1000,1000]; all real roots

2×2 — System 2×2

Cramer's Rule: x=Dₓ/D, y=Dᵧ/D

3×3 — System 3×3

Cramer's Rule with 3×3 determinants

bˣ — Exp & Log

bˣ=C → x=lnC/lnb; logₐx=C → x=aᶜ

sin — Trig Equations

Reference angle + quadrant rules, [0,2π)

⊙ — Conic Sections

Circle, parabola, ellipse, hyperbola

aₙ — Sequences

Arithmetic & geometric, nth term, sum

[A] — Matrices

det, inverse, multiply, add, transpose

Quadratic \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Discriminant \(\Delta=b^2-4ac\)

Vertex Form \(f(x)=a(x-h)^2+k\)

Vieta's \(x_1+x_2=-b/a,\;x_1x_2=c/a\)

2×2 Det \(D=a_1b_2-a_2b_1\)

Cramer's \(x=D_x/D,\;y=D_y/D\)

Log Change \(\log_b x=\ln x/\ln b\)

Exp Eq \(b^{kx}=C\Rightarrow x=\ln C/(k\ln b)\)

sin solutions \(x=\alpha+2\pi k,\;\pi-\alpha+2\pi k\)

Circle \((x-h)^2+(y-k)^2=r^2\)

Ellipse \(x^2/a^2+y^2/b^2=1\)

Parabola \(y=a(x-h)^2+k\)

Hyperbola \(x^2/a^2-y^2/b^2=1\)

Arith nth \(a_n=a_1+(n-1)d\)

Arith Sum \(S_n=n(a_1+a_n)/2\)

Geo nth \(a_n=a_1\cdot r^{n-1}\)

Geo Sum \(S_n=a_1(1-r^n)/(1-r)\)

Geo ∞ \(S_\infty=a_1/(1-r)\;|r|<1\)

2×2 Inv \(A^{-1}=(1/\det)\begin{pmatrix}d&-b\\-c&a\end{pmatrix}\)

f(x)Pre-Calculus Calculator