Key Features of Quadratic Graphs

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, representing the maximum or minimum value.

Front

What does the y-intercept represent in a quadratic graph?

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of the function when x = 0.

Front

What is the significance of the x-intercept in a quadratic graph?

Back

The x-intercept(s) are the points where the graph crosses the x-axis, indicating the values of x for which the function equals zero.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves, passing through the vertex.

Front

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

Back

For a quadratic in the form y = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What is the general shape of a quadratic graph?

Back

A quadratic graph is a parabola, which opens upwards if the coefficient of x^2 is positive and downwards if it is negative.

Front

What does the term 'maximum height' refer to in the context of a quadratic graph?

Back

The maximum height refers to the highest point on the graph, which occurs at the vertex if the parabola opens downwards.

Front

What does the term 'minimum height' refer to in the context of a quadratic graph?

Back

The minimum height refers to the lowest point on the graph, which occurs at the vertex if the parabola opens upwards.

Front

How do you determine the direction a parabola opens?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic equation y = ax^2 + bx + c; if 'a' is positive, it opens upwards, and if negative, it opens downwards.

Front

What is the formula for the vertex of a quadratic function in vertex form?

Back

In vertex form, y = a(x-h)^2 + k, the vertex is the point (h, k).