Answer:
Standard form: y = x^2 + 8x + 20
Explanation:
General equation of the vertex form:
The general equation of the vertex form of a quadratic is given by:
y = a(x - h)^2 + k, where:
- a is a constant determining whether,
- and (h, k) are the coordinates of the vertex.
General equation of the standard form:
The general equation of the standard form of a quadratic is given by:
y = ax^2 + bx + c, where:
- a, b, and c are constants.
Converting from vertex form to standard form:
Thus, we can convert to vertex form by expanding (x + 4)^2 and combining all like terms:
y = (x + 4)(x + 4) + 4
y = (x^2 + 4x + 4x + 16) + 4
y = x^2 + 8x + 20
Therefore, y = x^2 + 8x + 20 is the standard form of the quadratic, given that y = (x + 4)^2 + 4 is its vertex form.
Note that another way to write the equation in standard form is by setting y equal to 0:
0 = x^2 + 8x + 20.