Question

The coordinates of the turning point of the parabola whose equation is y = x2 — 6x + 8 are A. (3, 35) C. (-3, 35) B. (-3, —1) D. (3. —1)

Answer 1

D. (3. —1)

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), y_(v))`

In which

`x_(v) = -(b)/(2a)`

`y_(v) = -(\Delta)/(4a)`

Where

`\Delta = b^2-4ac`

If a<0, the vertex is a maximum point, that is, the maximum value happens at
`x_(v)`, and it's value is
`y_(v)`.

Turning point of a quadratic function:

The turning point of a quadratic function is the vertex.

y = x2 — 6x + 8

This means that
`a = 1, b = -6, c = 8`

Now, we find the vertex.

`x_(v) = -(b)/(2a) = -(-6)/(2(1)) = 3`

`\Delta = b^2-4ac = (-6)^2-4(1)(8) = 36 - 32 = 4`

`y_(v) = -(4)/(4(-1)) = -1`

(x,y) = (3,-1), and the correct answer is given by option D.