The Parabola Wears Its Features in Different Places

You'll learnto locate a parabola's vertex, roots, and y-intercept, then hand back the feature that was asked.

A parabola's vertex, roots, and y-intercept live in different places, and the same expression carries all of them. The points leak in four moves: misreading vertex form, inverting the discriminant's meaning, a sign slip in the formula, and handing back the wrong feature. Watch the vertex read straight off (h, k), the discriminant's sign set the count, every piece of the formula survive the trip, and the roots stay separate from the vertex and the intercept.

8 STEPS · 6 QUICK CHECKS · vertex, roots, and intercept are different places · v2

y = ax² + bx + c

Before you start

What you're looking at

A coordinate plane with the parabola y = x² − 2x − 8, its roots, vertex, and y-intercept each marked in its own place.

The question

Where does this parabola sit — its roots, its turning point, and where it meets the y-axis?

Watch for

The curve draws in and four points light up; notice each feature lives at a different spot on the same curve.

What the symbols mean

Each marked point is one feature: roots are where y = 0, the vertex is the turning point, the y-intercept where x = 0.

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