Vertex & Standard Forms

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 of the parabola.

Front

What does the 'a' in the vertex form of a quadratic function represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x - h)² + k to standard form, expand the equation to the form f(x) = ax² + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

How do you find the vertex from the standard form of a quadratic equation?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h.

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if its graph intersects the x-axis, which occurs when the discriminant (b² - 4ac) is greater than or equal to zero.

Front

How do you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined by calculating the discriminant (b² - 4ac): if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you find the y-intercept of a quadratic function in standard form?

Back

The y-intercept can be found by evaluating f(0), which gives the value of c in the equation y = ax² + bx + c.