Given y = (2x + 3)2, represent it in the standard form of the given quadratic equation.
Quadratic equations are equations that have a degree equal to two. They are represented as a parabola on the graph.
Answer: The standard form of the given equation y = (2x + 3)2 is y = 4x2 + 12x + 9.
Let's understand the solution in detail.
Given quadratic equation: y = (2x + 3)2.
Now, the standard form of a quadratic equation is given by y = ax2 + bx + c.
Now, to represent the given equation in standard form, we use the identity - (a + b)2.
Hence, (2x + 3)2 = (2x)2 + (2 × 2x × 3) + 32 = 4x2 + 12x + 9.
Hence, it is in the standard form y = ax2 + bx + c, where a = 4, b = 12 and c = 9.