Did you know?
Did you know that the vertex of a quadratic relation can be determined by partial factoring? To find the vertex of the relation y = -2x^2 - 8x + 1, we can follow these steps:
Step 1: Write down the given quadratic equation: y = -2x^2 - 8x + 1.
Step 2: Identify the quadratic coefficient (a), linear coefficient (b), and constant term (c). In this case, a = -2, b = -8, and c = 1.
Step 3: Use the formula x = -b/2a to find the x-coordinate of the vertex. Plugging in the values, x = -(-8)/2(-2) gives us x = 8/-4, which simplifies to x = -2.
Step 4: Substitute the x-coordinate of the vertex (x = -2) into the original equation to find the y-coordinate. By substituting x = -2 into y = -2x^2 - 8x + 1, we get y = -2(-2)^2 - 8(-2) + 1, which simplifies to y = -8 + 16 + 1. Hence, y = 9.
Step 5: Therefore, the vertex of the quadratic relation y = -2x^2 - 8x + 1 is (-2, 9).
