Characteristics of Quadratics Graphs

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, represented as (x, 0).

Front

How do you find the y-intercept of a quadratic equation?

Back

The y-intercept is found by evaluating the function at x = 0, giving the point (0, f(0)).

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What does the term 'axis of symmetry' refer to 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 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 does the coefficient 'a' in a quadratic equation indicate?

Back

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

Front

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

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the number and type of roots: two real roots, one real root, or no real roots.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x where the quadratic equation equals zero, also known as the solutions or x-intercepts.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.