Final answer:
To write the equation y=2x²+8x+3 in vertex form, we need to complete the square.
Step-by-step explanation:
To write the equation y=2x²+8x+3 in vertex form, we need to complete the square. The vertex form of a quadratic equation is given by y=a(x-h)²+k, where (h,k) represents the coordinates of the vertex.
Step 1: Factor out the coefficient of x² from the equation. y=2(x²+4x)+3
Step 2: Complete the square by adding and subtracting the square of half the coefficient of x. y=2(x²+4x+4)+3-8
Step 3: Simplify and rewrite the equation in vertex form. y=2(x+2)²-5