Question

3. What is the axis of symmetry for a parabola expressed by the quadratic equation of 2x2-8x+11?

©x=-2
©x=-2
© x=4
© x=-4

Answer 1

The axis of symmetry for a parabola can be found by looking at the equation of the parabola in the form of "y = a(x - h)^2 + k", where a, h, and k are constants. The axis of symmetry is the line that divides the parabola into two identical halves and is represented by the value of h.

In this case, the equation of the parabola is 2x^2 - 8x + 11, which is not in the vertex form. To express it in the vertex form, we have to complete the square.

2x^2 - 8x + 11

= 2(x^2 - 4x) + 11

= 2(x^2 - 4x + 4 - 4) + 11

= 2( (x-2)^2 - 4) + 11

Now we can see that the parabola is in the vertex form y = a(x-h)^2 + k, where a = 2, h = 2, and k = 3.

Therefore, the axis of symmetry for this parabola is x = 2

So the correct answer is: ©x=2

Answer 2

A) x = 2

Explanation:

The axis of symmetry of a parabola is a line that divides the parabola into two mirror-image halves and passes through the vertex of the parabola.

To find the axis of symmetry for a parabola expressed by a quadratic equation in the form ax² + bx + c, use the formula:

`x=-(b)/(2a)`

where "a" is the leading coefficient and "b" is the coefficient of the term in x.

In the case of the given equation 2x² - 8x + 11, the leading coefficient is 2 and the x-coefficient is -8.

Substitute these values into the axis of symmetry formula:

`\implies x=-((-8))/(2(2))`

`\implies x=(8)/(4)`

`\implies x=2`

Therefore, the axis of symmetry for a parabola expressed by the quadratic equation of 2x² - 8x + 11 is:

• x = 2