Graph the equation. y-4=1/4(x-1)²

Mathematics

2 answers:

Anastasy [175]3 years ago

7 0

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

Anastaziya [24]3 years ago

4 0

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)

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