Question

Graph the equation. y-4=1/4(x-1)²

Answer 1

y - 4 = ¹/₄(x - 1)²
y - 4 = ¹/₄(x - 1)(x - 1)
y - 4 = ¹/₄(x² - x - x + 1)
y - 4 = ¹/₄(x² - 2x + 1)
y - 4 = ¹/₄(x²) - ¹/₄(2x) + ¹/₄(1)
y - 4 = ¹/₄x² - ¹/₂x + ¹/₄
+ 4 + 4
y = ¹/₄x² - ¹/₂x + 4¹/₄
¹/₄x² - ¹/₄x + 4¹/₄ = 0
x = -(-¹/₄) +/- √(-¹/₄)² - 4(¹/₄)(4¹/₄))
2(¹/₄)
x = ¹/₄ +/- √(¹/₁₆ - 4¹/₄)
¹/₂
x = ¹/₄ +/- √(4³/₁₆)
¹/₂
x = ¹/₄ +/- 2.046
¹/₂
x = ¹/₂ + 4.092
x = ¹/₂ + 4.092 x = ¹/₂ - 4.092
x = 4.592 x = 3.592

Answer 2

y-4=1/4*(x-1)²
y=1/4(x-1)²+4
the parabola y=1/4x2 with vertex at the point (1;4),the branches up,x=1 is the axis of symmetry intersects the axis of the OY at the point (0;4 1/4)