An electronic engineer wants to know the vertex, focus, directrix and graph of (y + 7)^2= - 4x-2. Help the engineer solve and graph the parabola.
Answer (1)
Given equation:(y + 7)² = -4x - 2Step 1: Rewrite the equation into standard form.Move the constants so it looks like a standard parabola form:(y + 7)² = -4(x + 0.5)This matches the standard form of a sideways parabola:(y - k)² = 4p(x - h)From the equation, we can identify:h = -0.5k = -74p = -4 → p = -1Step 2: Identify key parts.Vertex: (h, k) = (-0.5, -7)Focus: (h + p, k) = (-0.5 + (-1), -7) = (-1.5, -7)Directrix: x = h - p = -0.5 - (-1) = 0.5Direction of opening: Since p is negative, the parabola opens to the leftSummary:Vertex: (-0.5, -7)Focus: (-1.5, -7)Directrix: x = 0.5Opens: to the left
