SAT Math: Intercept Form of Quadratics
31+ practice questions in Praczo
The concept, explained
- 1
Intercept form (or factored form) is y = a(x - p)(x - q), where p and q are the x-intercepts (or roots/zeros) of the parabola.
- 2
The x-coordinate of the vertex is always exactly halfway between the intercepts: x = (p + q) / 2.
- 3
If the SAT gives you the intercepts and another point, plug them into the form to solve for "a".
- 4
If a factored form has a squared term like y = (x - 3)², the graph is tangent to the x-axis at x = 3 (it touches and turns around).
- 5
The sign inside the parentheses is the OPPOSITE of the actual intercept coordinate.
- ✗ Thinking y = (x + 4)(x - 2) has intercepts at 4 and -2 (they are actually -4 and 2).
- ✗ Assuming the vertex is one of the intercepts rather than the midpoint between them.
SAT-style practice
A parabola passes through the x-axis at (-2, 0) and (6, 0). What is the x-coordinate of its vertex?
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