Quadratic equations are a major component of the "Passport to Advanced Math" domain on the SAT. This guided path will teach you the essential skills, from algebraic solving methods to the crucial interpretation of their graphs (parabolas).
Start with the core definition of a quadratic equation and use our interactive verifier to understand what the "roots" of an equation represent.
A Quadratic Equation has the form $$ ax^2 + bx + c = 0 $$
The Roots are the specific values of 'x' that make the equation true (equal to zero). Every quadratic has exactly two roots.
Learn the step-by-step process of factoring quadratic expressions to find the roots, a crucial skill for the no-calculator section.
Goal: Rewrite $$ ax^2 + bx + c = 0 $$ into $$ (x+m)(x+n) = 0 $$.
Shortcut (when a=1): Find two numbers that multiply to 'c' and add to 'b'.
Master the universal tool for solving any quadratic equation. Our interactive calculator shows you how to apply the formula step by step.
The universal method for any quadratic:
The term inside the root, $$ b^2 - 4ac $$, is called the Discriminant.
Visually connect the discriminant ($$b^2-4ac$$) to the graph of a parabola and understand how it determines the number of real solutions.
The Discriminant ($$ b^2 - 4ac $$) determines how many times the parabola crosses the x-axis.
$$ x^2 - 4x + 3 = 0 $$
$$ D = 4 $$ (Positive)
Crosses x-axis twice.
Learn the step-by-step process of translating a real-world SAT word problem (like a projectile's path) into a quadratic function.
Build the equation for a rocket launched from 80ft at 64 ft/s.
Model: $$ h(t) = -16t^2 + v_0t + h_0 $$
The problem states velocity is 64 ft/s.
$$ v_0 = 64 $$
The rocket starts from a platform 80 ft high.
$$ h_0 = 80 $$
Substitute values into the model:
Put your understanding of SAT Quadratic Equations: A Guide to Advanced Math to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
