SOLUTION: Consider the function: f(x)=x²-8x+15 a. What are the zeros of the function (use factoring)? b. What is the axis of symmetry of the parabola? c. What is the vertex of the parabol

Algebra ->  Rational-functions -> SOLUTION: Consider the function: f(x)=x²-8x+15 a. What are the zeros of the function (use factoring)? b. What is the axis of symmetry of the parabola? c. What is the vertex of the parabol      Log On


   

Question 1010113: Consider the function: f(x)=x²-8x+15
a. What are the zeros of the function (use factoring)?
b. What is the axis of symmetry of the parabola?
c. What is the vertex of the parabola (put it in vertex form)?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Both (a) and (b) can be done through factoring and using the factored form.

Solving part (c) will use Completing the Square. See the lesson.
f%28x%29=x%5E2-8x%2B16%2B15-16
Finish this.



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Vertex is (4,1).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the function: f(x)=x²-8x+15
a. What are the zeros of the function (use factoring)?
b. What is the axis of symmetry of the parabola?
c. What is the vertex of the parabola (put it in vertex form)?
f%28x%29+=+x%5E2+-+8x+%2B+15

a. f%28x%29+=+%28x+-+5%29%28x+-+3%29

   Zeroes, or highlight_green%28matrix%281%2C3%2Cx+=+5%2C+OR%2C+x+=+3%29%29



b. The x-coordinate of the vertex or the axis of symmetry is at: x+=+-b%2F%282a%29, which in this case is: x+=+-+-+8%2F%282+%2A+1%29, or x+=+8%2F2, or highlight_green%284%29



c. You don't have to put it in vertex form to find the vertex, especially since the x-coordinate of the vertex is now known (x+=+4). All

   that's needed now is to substitute 4 for x into the equation, and the y-coordinate of the vertex will also be known, which by the way is: y = - 1.

   Vertex is therefore: (highlight_green%284%29%22%2C%22highlight_green%28-+1%29)

However, since it's requested that you put the parabola in vertex form: f%28x%29+=+a%28x+-+h%29%5E2+%2B+k%29, then by all means do so.