Key Features of Quadratic Graphs (1)

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point of the parabola, represented as an ordered pair (h, k) in the vertex form of the equation y = a(x - h)² + k.

Front

What does the ordered pair (2, -4) represent in the context of a quadratic graph?

Back

It is the vertex of the parabola.

Front

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

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, b) where b is the value of the function when x=0.

Front

What is the equation for the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is given by the equation x = h, where (h, k) is the vertex of the parabola.

Front

If the vertex of a parabola is (2, −3), what is the axis of symmetry?

Back

The axis of symmetry is x = 2.

Front

What is the general form of a quadratic equation?

Back

The general form is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

If the coefficient 'a' in the equation y = ax² + bx + c is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What are the x-intercepts of a quadratic graph?

Back

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

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.