3-1 Key Features of Parabolas

Front

What is the vertex of a parabola?

Back

The highest or lowest point of a parabola.

Front

What does the axis of symmetry represent in a parabola?

Back

A vertical line that divides the parabola into two mirror-image halves.

Front

What is the y-intercept of a parabola?

Back

The point where the parabola crosses the y-axis.

Front

What are x-intercepts in a parabola?

Back

The points where the parabola crosses the x-axis.

Front

What does it mean if a parabola opens upwards?

Back

It has a minimum vertex and the arms of the parabola extend upwards.

Front

What does it mean if a parabola opens downwards?

Back

It has a maximum vertex and the arms of the parabola extend downwards.

Front

How can you determine if a parabola has a maximum or minimum?

Back

By looking at the direction it opens: upwards indicates a minimum, downwards indicates a maximum.

Front

What is the standard form of a quadratic equation?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the significance of the coefficient 'a' in the quadratic equation?

Back

It determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width.

Front

How do you find the vertex of a parabola given in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.