Jessi and her dad played tennis on Saturday morning. The number line represents the tennis court, with the net located at 0.5. The distance the ball traveled on each of Jessi's first four serves is represented on the number line and labeled with the serve number. Which best represents the part of the distance between Jessi and Dad that her first serve traveled? 0.94 0.60 0.90 0.47

The x-intercepts of a graph are found by factoring.  Set y = 0 because the x-intercepts exist when y = 0.  Put this into the quadratic formula to factor.  Like this:   which simplifies to .  The square root of 64 is 8, so the values we find for x are -1 or 3/5.  Because this is a positive parabola, it opens upwards, like a cup, and a cup has a bottom.  So the vertex is a minimum value.  If it was a negative parabola it would open downwards like a mountain and mountains have top.  The coordinates of the vertex can be found by completing the square.  We also could have factored it by completing the square as well!  Should have read that first...but here's how we do that... Move the constant over to the other side of the equals sign.  The rule for completing the square is that the leading coefficient has to be a 1 and it's a 5.  So we will factor out the 5:  .  Take half the linear term, square it and add it to both sides.  Out linear term is 2/5.  Half of 2/5 is 2/10 or 1/5.  1/5 squared is 1/25.  We will add it into the parenthesis, but don't forget about that 5 hanging out front there, refusing to be ignored.  It is a multiplier, so we multiply 5 by 1/25 and add that to the right.  Like this: .  Doing the math on the right and then rewriting the left using the perfect square binomial we created for the purpose of finding the vertex we have  .  Move the constant back over by subtraction to get .  The vertex is .  Graph it by plotting the x-intercepts and the vertex and the y-intercept.  Find other points and graph them if needed.