Transforming Standard to 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 convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

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, dividing it into two mirror-image halves.

Front

What does it mean if a parabola opens 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 if a parabola opens downwards?

Back

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

Front

Identify the vertex of the parabola given by the equation y = 2(x-3)² + 5.

Back

The vertex of the parabola is (3, 5).

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 whether it opens up or down.

Front

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

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

Front

What is the formula for completing the square?

Back

To complete the square for ax² + bx, take (b/2)², add and subtract it inside the equation.

Front

Convert the equation y = x² + 6x + 8 into vertex form.

Back

y = (x + 3)² - 1.