Respuesta :
Answer:
y = (x - 3)² + 7 is a minimum vertex at (3, 7)
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form using completing the square
• add/ subtract ( half the coefficient of the x-term )² to x² - 6x
y = x² + 2(- 3)x + 9 - 9 + 16 = (x - 3)² + 7 ← in vertex form
with vertex = (3, 7 )
Since coefficient of x² term > 0 then minimum
The modified equation in square will be: y = (x - 3)² + 7 and the vertex of it is minimum as per the equation of a parabola in vertex form.
What is the equation of a parabola in vertex form?
The equation of a parabola in vertex form is: y = a(x - h)² + k.
Here, (h, k) are the coordinates of the vertex and a is the coefficient.
Given equation: y = x² - 6x + 16
⇒ y = x² - 2 × x ×3 + 3² + 7
⇒ y = (x - 3)² + 7
Therefore, vertex is at (3, 7) and coefficient 'a' is = 1.
As a > 0, therefore, the vertex is a minimum.
Learn more about the equation of a parabola in vertex form here: https://brainly.com/question/17007204
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