Interpreting Vertex Form and Standard 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 axis of symmetry for a quadratic equation in standard form?

Back

The axis of symmetry for a quadratic equation in standard form y = ax² + bx + c is given by the formula x = -b/(2a).

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

Convert the standard form equation y = x² + 4x into vertex form.

Back

y = (x + 2)² - 4.

Front

Convert the standard form equation y = x² - 8x + 1 into vertex form.

Back

y = (x - 4)² - 15.

Front

What is the vertex of the parabola represented by the equation y = 3(x - 1)² + 2?

Back

The vertex is (1, 2).

Front

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

Back

By examining the coefficient 'a' in the vertex form; if 'a' is positive, it opens upwards, and if 'a' is negative, it opens downwards.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.