Exploring Graphs of Quadratics

Front

What are the solutions of the quadratic equation represented by the graph?

Back

The solutions are the x-intercepts of the graph.

Front

What does the axis of symmetry represent in a quadratic graph?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

How do you find the vertex of a quadratic function from its graph?

Back

The vertex is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the vertex of the quadratic function f(x) = -x² - 4x + 12?

Back

The vertex is (-2, 16).

Front

Does the quadratic function y = 2x² + 7x + 5 have a maximum or minimum value?

Back

It has a minimum value because the coefficient of x² is positive.

Front

What is the standard form of a quadratic equation?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the standard form is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a).

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of f(0).

Front

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

Back

Set f(x) = 0 and solve for x using factoring, completing the square, or the quadratic formula.