Converting Standard to Vertex Form

Front

What is vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by: f(x) = 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 (ax² + bx + c) to vertex form (a(x - h)² + k), complete the square.

Front

What is the vertex of the parabola represented by the equation f(x) = (x - 1)² - 4?

Back

The vertex is (1, -4).

Front

Given the equation y = 2(x - 3)² - 9, what is the value of 'a'?

Back

The value of 'a' is 2.

Front

What does the 'a' value in vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

Front

Convert the equation y = -x² + 10x - 4 to vertex form.

Back

y = -(x - 5)² + 21.

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.

Front

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

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form ax² + bx + c.

Front

What is the vertex of the parabola represented by the equation y = -2(x - 6)² - 67?

Back

The vertex is (6, -67).

Front

Convert the equation y = 4x² - 32x + 2 to vertex form.

Back

y = 4(x - 4)² - 62.