Intermediate Algebra | 34.6: Graphing Parabolas When A Is Negative
Full course — free exercises, Feynman reviews, and AI-graded feedback:
https://ludium.ai/courses/intermediat...
When the leading coefficient of a quadratic is negative, standard factoring breaks down — unless you apply one key technique before you begin. This video walks through the complete process of graphing y = -x² + 5x + 6, covering the vertex, y-intercept, and x-intercepts in the correct order and explaining exactly why that order matters.
Key concepts covered:
How the sign of the leading coefficient A determines whether a parabola opens upward or downward
Applying the vertex formula x = -B/(2A) when A is negative, including careful handling of double negatives
Why the vertex is a maximum point when A is negative
Fraction arithmetic in vertex calculations: converting to a common denominator and combining terms
Y-intercept: setting x = 0 and recognizing the result as the constant term C
The sign-flip technique: dividing every term by -1 to convert a negative leading coefficient before factoring
Why sign-flipping is only valid for x-intercepts — both sides of the equation equal zero, so solutions are preserved
Factoring x² - 5x - 6 = 0 by identifying two numbers with product -6 and sum -5
A side-by-side comparison showing which features come from the original equation and which come from the sign-flipped version
Assembling the complete graph with vertex, both intercepts, and axis of symmetry
Using the quadratic formula as a fallback when factoring fails after flipping signs