Key Features of Quadratic Graphs

Front

What is a quadratic graph?

Back

A quadratic graph is a graph of a quadratic function, which is a polynomial function of degree 2, typically in the form y = ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction of the parabola.

Front

What is the y-intercept of a quadratic graph?

Back

The y-intercept is the point where the graph intersects the y-axis, found by setting x = 0 in the equation.

Front

What are the roots or x-intercepts of a quadratic graph?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.

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 equation x = -b/(2a).

Front

What is the maximum height of a projectile represented by a quadratic graph?

Back

The maximum height is the y-value of the vertex when the parabola opens downward.

Front

What is the minimum height of a projectile represented by a quadratic graph?

Back

The minimum height is the y-value of the vertex when the parabola opens upward.