This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the coordinates of the turning points for each function: a) y = x^2 + x + c Step 1: Find the x-coordinate of the turning point using the formula x = -(b)/(2a). For y = x^2 + x + c, we have a=1, b=1. x = -(1)/(2(1)) = -(1)/(2) Step 2: Substitute the x-coordinate back into the original equation to find the y-coordinate. y = (-(1)/(2))^2 + (-(1)/(2)) + c y = (1)/(4) - (1)/(2) + c y = (1)/(4) - (2)/(4) + c y = -(1)/(4) + c The turning point is (-(1)/(2), c - (1)/(4)). b) y = 3x^2 - 4x + 5 Step 1: Find the x-coordinate of the turning point using the formula x = -(b)/(2a). For y = 3x^2 - 4x + 5, we have a=3, b=-4. x = -((-4))/(2(3)) = (4)/(6) = (2)/(3) Step 2: Substitute the x-coordinate back into the original equation to find the y-coordinate. y = 3((2)/(3))^2 - 4((2)/(3)) + 5 y = 3((4)/(9)) - (8)/(3) + 5 y = (12)/(9) - (8)/(3) + 5 y = (4)/(3) - (8)/(3) + (15)/(3) y = (4 - 8 + 15)/(3) y = (11)/(3) The turning point is ((2)/(3), (11)/(3)). Send me the next one 📸