Transforming Standard to Vertex Form

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

What is the vertex of the parabola given by the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4).

Front

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

Back

y = (x + 2)² - 4.

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is called a parabola.

Front

Convert f(x) = x² + 12x - 2 into vertex form.

Back

f(x) = (x + 6)² - 38.

Front

What does the vertex of a parabola represent?

Back

The vertex represents the highest or lowest point of the parabola, depending on its orientation.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

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

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the significance of the 'a' value in the quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is the formula for the axis of symmetry of a parabola in standard form?

Back

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