Find the vertex form of the function. Then find each of the following.(A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range s ( x ) = − 5 x 2 − 30 x − 42s(x) = (Answer has to be given in vertex form).

Question

Find the vertex form of the function. Then find each of the following.(A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range  s  (  x  )  =  −  5      x    2    −  30  x  −  42s(x) = (Answer has to be given in vertex form).

Jaxson White · Accepted Answer

The equation of a quadratic in vertex form is:  y  =  a  (  x  −  h      )    2    +  k  .The vertex is at the point (h, k).You must complete the square for this.  s  (  x  )  =  −  5      x    2    −  30  x  −  42Take out a -5 to get:  −  5  (      x    2    +  6  x  +  (      42    5    )  )Complete the square :  s  (  x  )  =  −  5  (      x    2    +  6  x  +  (  6      /    3      )    2    +  (  42      /    5  )  −  (  6      /    3      )    2    )    s  (  x  )  =  −  5  (      x    2    +  6  x  +  9  +  (  42      /    5  )  −  9  )    s  (  x  )  =  −  5  [  (  x  +  3      )    2    (  42      /    5  )  −  (  45      /    5  )  ]    s  (  x  )  =  −  5  [  (  x  +  3      )    2    −  (  3      /    5  )  ]    s  (  x  )  =  −  5  (  x  +  3      )    2    +  3.The y-intercept is when x = 0, it&#039;s:  y  =  −  5  (  3      )    2    +  3  =  −  45  +  3  =  −  42.y-intercept is y = -42.The x-intercept(s) are when y = 0, i.e. when s(x) = 0.  0  =  −  5  (  x  +  3      )    2    +  3  −  3  =  −  5  (  x  +  3      )    2    3      /    5  =  (  x  +  3      )    2    x  +  3  =  +      (        3    5    )  x  =  −  3  +      (        3    5    )The two x-intercepts are:   x  =  −  3  +      (        3    5    )     x  =  −  3  −      (        3    5    )vertex is at : (-3, 3).There is a max since the parabola is upside down. The max is the same as the vertex, and it&#039;s atx = 3.Range is from negative infinity to the vertex.  (  −  ∞  ,  3  ]

Find the vertex form of the function. Then find each of the following. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range s(x) = -5x^2 - 30x - 42 s(x) = (Answer has to be given in vertex form).

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