Graphing quadratics from vertex form

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

To find the vertex from the standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What does it mean for a parabola to open upwards?

Back

A parabola opens upwards if the coefficient 'a' in the vertex form y = a(x - h)² + k is positive.

Front

What does it mean for a parabola to open downwards?

Back

A parabola opens downwards if the coefficient 'a' in the vertex form y = a(x - h)² + k is negative.

Front

Given the equation y = 2(x - 3)² + 1, what is the vertex?

Back

The vertex is (3, 1).

Front

How can you determine the direction a parabola opens from its equation?

Back

Look at the coefficient 'a' in the vertex form; if 'a' is positive, it opens up; if 'a' is negative, it opens down.

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 its direction.

Front

If the vertex of a parabola is at (4, -2), what is the vertex form of the equation if it opens upwards?

Back

The vertex form is y = a(x - 4)² - 2, where 'a' is a positive number.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

How do you convert from vertex form to standard form?

Back

Expand y = a(x - h)² + k to get y = ax² - 2ahx + (ah² + k).