Question

Y = 2x^2-12x+25 write in vertex form plz show work

Answer 1

The vertex form of y = 2x² - 12x + 25 is y = 2(x - 3)² + 7

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

• (h , k) are the coordinates of the vertex point
• a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
• $h=\frac{-b}{2a}$
• k is the value of y when x = h

∵ y = 2x² - 12x + 25

∵ y = ax² + bx + c

∴ a = 2 , b = -12 , c  = 25

∵ $h=\frac{-b}{2a}$

∴ $h=\frac{-(-12)}{2(2)}$

∴ $h=\frac{12}{4}$

∴ h = 3

To find k substitute y by k and x by 3 in the equation above

∵ k is the value of y when x = h

∵ h = 3

∴ k = 2(3)² - 12(3) + 25 = 7

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 2 , h = 3 , k = 7

∴ y = (2)(x - 3)² + 7

∴ y = 2(x - 3)² + 7

The vertex form of y = 2x² - 12x + 25 is y = 2(x - 3)² + 7

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