Barron's SAT Math Workbook by Lawrence S. Leff

Author:Lawrence S. Leff
Language: eng
Format: epub
Publisher: Barron's Educational Series
Published: 2016-10-21T04:00:00+00:00

VERTEX OF A PARABOLA

A line can be drawn through a parabola that divides it into two mirror image parts. The line of symmetry intersects the parabola at its vertex. The vertex is either the highest or the lowest point on the parabola. For the parabola y = ax2 + bx + c,

■If a > 0, the parabola opens up and the vertex is the lowest (minimum) point on the curve. See Figure 5.1. The graph of y = x2 − x − 6 is a parabola that opens up since the coefficient of the x2-term is positive.

Figure 5.1 Graph of y = ax2 + bx + c with a > 0

■If a < 0, the parabola opens down and the vertex is the highest (maximum) point on the curve. See Figure 5.2. The graph of y = −2x2 − x + 8 is a parabola that opens down since the coefficient of the x2-term is negative.

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