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 does the y-intercept represent in a quadratic graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the value of y when x = 0.

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph, depending on the direction of the parabola (opening upwards or downwards).

Front

How do you find the x-intercepts of a quadratic graph?

Back

The x-intercepts can be found by setting the quadratic equation to zero and solving for x (i.e., finding the roots of the equation).

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, passing through the vertex.

Front

What does the term 'parabola' refer to?

Back

A parabola is the U-shaped graph of a quadratic function, which can open upwards or downwards.

Front

What is the significance of the ordered pair (0, c) in a quadratic graph?

Back

The ordered pair (0, c) represents the y-intercept of the graph, where c is the value of the function when x = 0.

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex of the parabola, calculated using the formula x = -b/(2a) for the x-coordinate.

Front

What does it mean if a quadratic graph has no real x-intercepts?

Back

If a quadratic graph has no real x-intercepts, it means the graph does not cross the x-axis, indicating that the quadratic equation has no real solutions.

Front

What is the standard form of a quadratic function?

Back

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