Standard to Vertex Form

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function 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 function from standard form to vertex form?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

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

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

Convert f(x) = 2x² + 8x + 5 to vertex form.

Back

f(x) = 2(x + 2)² + 1.

Front

What is the vertex of the parabola given by f(x) = 3(x - 1)² - 4?

Back

The vertex is (1, -4).

Front

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

Back

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

Front

Convert y = x² - 4x + 6 into vertex form.

Back

y = (x - 2)² + 2.

Front

What are the roots of a quadratic function?

Back

The roots (or x-intercepts) are the values of x where the function equals zero, found by solving the equation ax² + bx + c = 0.

Front

What is the significance of the vertex in a parabola?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.