IDNLearn.com helps you find the answers you need quickly and efficiently. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

Graph the equation. y-4=1/4(x-1)²

Sagot :

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)
View image Albina
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