Quadratics: Graphing, Changing, Writing

Front

What is the axis of symmetry of a parabola given by the equation y = a(x - h)^2 + k?

Back

The axis of symmetry is the vertical line x = h.

Front

What does the value of 'a' indicate in the quadratic function y = a(x - h)^2 + k?

Back

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

Front

How do you find the vertex of a parabola in vertex form y = a(x - h)^2 + k?

Back

The vertex is the point (h, k).

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax^2 + bx + c.

Front

How do you convert from vertex form to standard form?

Back

Expand the equation y = a(x - h)^2 + k to get y = ax^2 - 2ahx + (ah^2 + k).

Front

What is the maximum or minimum value of a parabola?

Back

The maximum or minimum value occurs at the vertex, depending on the sign of 'a'.

Front

Given the equation y = -2(x + 4)^2 + 5, what is the vertex?

Back

The vertex is (-4, 5).

Front

What is the formula for the axis of symmetry for the quadratic equation y = ax^2 + bx + c?

Back

The axis of symmetry is given by x = -b/(2a).

Front

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

Back

If 'a' is positive, it has a minimum value; if 'a' is negative, it has a maximum value.

Front

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

Back

The discriminant (b^2 - 4ac) determines the number of real roots: positive means 2 roots, zero means 1 root, negative means no real roots.