Select ALL the correct answers.

Consider the following quadratic equation.

y=x²-8x+4

Which of the following statements about the equation are true?

When y = 0, the solutions of the equation are x=8±2√2.

The extreme value of the graph is at (8,-4).

When y = 0, the solutions of the equation are x=4±2√3.

The extreme value of the graph is at (4,-12).

The graph of the equation has a minimum.

The graph of the equation has a maximum.

Statements 3, 4 and 5 are true.

Step-by-step explanation:

x^2 - 8x + 4

Using the quadratic formula:

x = [ - (-8) + / - √ ((-8) ^2 - 4*1*4) ] / 2

= (8 + / - √ (64 - 16)) / 2

= 4 + / - √48 / 2

= 4 + / - 4√3/2

= 4 + / - 2√3.

So the third statement is true.

Converting to vertex form:

x^2 - 8x + 4

= (x - 4) ^2 - 16 + 4

= (x - 4) ^2 - 12

So the extreme value is at (4, - 12)

So the fourth statement is true.

The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.