Properties of Quadratic Graphs

Front

What direction does the graph of a quadratic equation open if the leading coefficient is negative?

Back

The graph opens down.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

How can you determine if a parabola opens up or down?

Back

If the leading coefficient (a) is positive, it opens up; if negative, it opens down.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation y = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What does the term 'roots' refer to in a quadratic equation?

Back

Roots are the values of x that make the equation equal to zero, also known as x-intercepts.

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.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient determines the direction of the parabola's opening and its width.