Respuesta :

susanwiederspan
To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c.

We are given two different solutions of the equation.

First, (2, 0). 
[tex]0=(2)^2+2b+c\\-4=2b+c[/tex]

Second, (0, 14).
[tex]14=(0)^2+0b+c\\c=14[/tex]

So we have a value (14) for c. We can substitute that into our first equation to find b.

[tex]-4=2b+c\\-4=2b+14\\-18=2b\\b=-9[/tex]

We can now plug in our values for b and c into the equation to get its standard form.

[tex]y=x^2-9x+14[/tex]

To find the vertex, we can convert this equation to vertex form [tex]y=a(x-h)^2+k[/tex] by completing the square.

[tex]y=x^2-9x+14[/tex]

[tex]y=x^2-9x+(-4.5)^2+14-(-4.5)^2[/tex]

[tex]y=x^2-9x+20.25+14-20.25[/tex]

[tex]y=(x-4.5)^2-6.25[/tex]

Thus, the vertex is (4.5, –6.25).

We can confirm the solution graphically (see attachment).
Ver imagen susanwiederspan
Cricetus

The x-coordinate of turning point will be "[tex]\frac{9}{2}[/tex]".

According to the question,

  • [tex]y = x^2+bx+c[/tex]

Curve passes,

  • [tex](2,0)[/tex] and,
  • [tex](0,14)[/tex]

By putting (0, 14), we get

→ [tex]14=0+0+c[/tex]

    [tex]c = 14[/tex]

then,

→ [tex]y = x^2+bx+14[/tex]

By putting (2, 0), we get

→    [tex]0=4+2b+14[/tex]

  [tex]-2b = 18[/tex]

      [tex]b = -\frac{18}{2}[/tex]

         [tex]= -9[/tex]

then,

→ [tex]y = x^2-9x+14[/tex]

Finding [tex]\frac{dy}{dx}[/tex],

→ [tex]\frac{dy}{dx} = 2x-9[/tex]

For turning point,

→       [tex]\frac{dy}{dx} =0[/tex]

  [tex]2x-9=0[/tex]

        [tex]2x = 9[/tex]

          [tex]x = \frac{9}{2}[/tex]

Thus the above answer is correct.

Learn more:

https://brainly.com/question/15180519

Otras preguntas