How do you find the axis of symmetry and the vertex for the line #y = x^2 - 6x +11#?

Answer 1

#x=3" and "(3,2)#

#"given the equation of a quadratic in "color(blue)"standard form"#
#•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0#
#"then the x-coordinate of the vertex which is also the"# #"equation of the axis of symmetry is"#
#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#
#y=x^2-6x+11" is in standard form"#
#"with "a=1,b=-6" and "c=11#
#x_("vertex")=-(-6)/2=3#
#"substitute this value into the equation for y"#
#y_("vertex")=3^2-(6xx3)+11=2#
#color(magenta)"vertex "=(3,2)#
#"axis of symmetry is "x=3# graph{(y-x^2+6x-11)(y-1000x+3000)=0 [-10, 10, -5, 5]}
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Answer 2

To find the axis of symmetry for the quadratic equation y = x^2 - 6x + 11, use the formula: x = -b / (2a). In this equation, 'a' is the coefficient of x^2 (which is 1), and 'b' is the coefficient of x (which is -6). So, x = -(-6) / (2 * 1) = 3. To find the vertex, substitute the value of x = 3 into the equation y = x^2 - 6x + 11. So, y = (3)^2 - 6(3) + 11 = 2. Therefore, the axis of symmetry is x = 3, and the vertex is (3, 2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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