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4-5.
  1. For each equation in parts (a) through (d) below, find the input value that gives the smallest possible output. In other words, find the x-value of the lowest point on the graph. Then find the input value that gives the largest possible output (or the x-value of the highest point on the graph). Homework Help ✎

    1. y = (x − 2)2

    2. y = x2 + 2

    3. y = (x + 3)2

    4. y = −x2 + 5

    5. Where on the graphs of each of the above equations would you find the points with the smallest or largest y-values?

Are there any x-values that yield a negative number?

It is impossible for y to be negative in this case. In turn, what is the lowest value y can be? Can y equal 0?

When x is equal to 2, y is equal to 0, which is the smallest possible output.

Does this parabola open upward or downward?

It opens upward. Therefore, there will be a smallest output.

Lowest point: x = 0, y = 2

See part (a).

See part (b). Notice the negative sign in front of the x2 term. How does that change the parabola?