Vertex to Standard/ Standard to Vertex

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by: f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form (f(x) = a(x - h)^2 + k) to standard form, expand the equation: f(x) = a(x^2 - 2hx + h^2) + k = ax^2 - 2ahx + (ah^2 + k).

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

What is the vertex of the parabola represented by f(x) = 3(x - 5)^2 - 1?

Back

The vertex of the parabola is (5, -1).

Front

Convert f(x) = 4x^2 - 32x + 2 to vertex form.

Back

f(x) = 4(x - 4)^2 - 62.

Front

What is the process to find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in standard form (f(x) = ax^2 + bx + c), use the formula: h = -b/(2a) and then substitute h back into the function to find k.

Front

What does the 'a' value in a quadratic equation indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

Convert y = -2(x - 4)^2 + 2 into standard form.

Back

y = -2x^2 + 16x - 30.

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 convert f(x) = x^2 + 12x - 2 to vertex form?

Back

Complete the square: f(x) = (x + 6)^2 - 38.