Question

y = 2x2-12x+25 write in vertex form and 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 a quadratic function is y = a(x - h)² + k, where

• (h , k) are the coordinate of the vertex point
• a is the leading coefficient (coefficient of x²)
• If y = ax² + bx + c, then $h=\frac{-b}{2a}$
• k = f(h) that means 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

∵ k = f(h)

∴ k = f(3)

∵ y = 2x² - 12x + 25

- Substitute x by 3 to find k

∴ k = 2(3)² - 12(3) + 25

∴ k = 18 - 36 + 25

∴ k = 7

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

∵ a = 2 , h = 3 , k = 7

∴ y = 2(x - 3)² + 7

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

Learn more:

You can learn more about the quadratic function in brainly.com/question/9390381

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