book Maths Puzzle Numerical Ability

A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist抯 average rate for the round trip in miles per hour?

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Mixing Antifreeze
A radiator holds 5 gallons of fluid. It is full with a 15% solution, how much fluid should be drained and replaced with 65% antifreeze mixture to result in a 40 Hello to all!

Could someone kindly explain to me clearly, how to find the Vertex and intercepts of:

y = -2x^2 + 8x.

The book's answers are: Vertex(2,8):, intercepts are: