Standard Form to Vertex Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

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 (y = a(x - h)² + k), you can complete the square.

Front

What is the vertex of a parabola in vertex form?

Back

The vertex of a parabola in vertex form y = a(x - h)² + k is the point (h, k).

Front

What does the 'a' value in the vertex form of a quadratic indicate?

Back

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

Front

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

Back

y = (x + 2)² - 4.

Front

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

Back

The vertex is (-5, -4).

Front

Convert the equation y = x² + 4x + 11 into vertex form.

Back

y = (x + 2)² + 7.

Front

Which of the following is a standard form of a quadratic equation?

Back

y = ax² + bx + c.

Front

Convert the equation f(x) = x² - 8x + 1 into vertex form.

Back

f(x) = (x - 4)² - 15.

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 the direction it opens.