y = 2x² - 12x + 25 in the vertex form is y = 2(x - 3)² + 7
Step-by-step explanation:
The vertex form of a quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinate of the vertex point
- a is the coefficient coefficient of x²
- [tex]h=\frac{-b}{2a}[/tex]
- k = y when x = h
∵ y = ax² + bx + c
∵ y = 2x² - 12x + 25
∴ a = 2 , b = -12 , c = 25
∵ [tex]h=\frac{-b}{2a}[/tex]
∴ [tex]h=\frac{-(-12)}{2(2)}[/tex]
∴ [tex]h=\frac{12}{4}[/tex]
∴ h = 3
∵ k = y at x = h
∵ h = 3
∴ k = y at x = 3
∵ y = 2x² - 12x + 25
- Substitute x by 3
∴ 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
y = 2x² - 12x + 25 in the vertex form is y = 2(x - 3)² + 7
Learn more:
You can learn more about the quadratic equation in brainly.com/question/1332667
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