Quadratic Graphs

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the coefficient 'a' in a quadratic equation determine about the parabola?

Back

The coefficient 'a' determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the maximum value of a parabola that opens downwards?

Back

The maximum value of a parabola that opens downwards is the y-coordinate of its vertex.

Front

What is the minimum value of a parabola that opens upwards?

Back

The minimum value of a parabola that opens upwards is the y-coordinate of its vertex.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

You can determine if a quadratic function has a maximum or minimum value by looking at the sign of the coefficient 'a': if 'a' is positive, it has a minimum; if 'a' is negative, it has a maximum.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.