Question

Hi. I need help with this questions.
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Answer 1

• p = 3, q = 2/3, r = 14/3

Explanation:

Given equation

• y = 3x² - 4x + 6

To find

The constants p, q, r when

• 3x² - 4x + 6 = p(x - q)² + r

Solution

The least value is at vertex of the parabola ax² + bx + c, with positive a

x and y -coordinates of the vertex is:

• x = -b/2a = - (-4)/(2*3) = 2/3
• y = 3(2/3)² - 4(2/3) + 6 = 3(4/9) - 8/3 + 6 = 4/3 - 8/3 + 6 = 14/3

The vertex form is:

• y = a(x-h)² + k, where (h, k) is the vertex

Applying the same formula to our equation:

• 3x² - 4x + 6 = 3(x - 2/3) + 14/3

The constants p, q and r are:

• p = 3, q = 2/3, r = 14/3