Question 698·Easy·Math

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Let the function $g$ be defined by $g(x) = -2(x-1)^2 + 7$ . What is the maximum value of $g(x)$ ?

Your answer

A quadratic in vertex form, $a(x-h)^2+k$ , shows its turning point without graphing. The square is zero at $x=h$ , so the output there is $k$ ; the sign of $a$ tells you whether that output is a maximum or a minimum. Keep the input where the turn happens separate from the output the question asks for.

Hints

Hint 1
In vertex form, the squared part becomes zero at the turning point. What input makes $(x-1)^2$ zero?
Hint 2
A square is never negative. Multiplying it by a negative number makes a term that is zero or negative, so can it ever raise the output above the constant?

Step-by-step

Read the maximum from vertex form
Step 1
Find where the square is zero
No Desmos needed. The function is already in vertex form, which shows its turning point. The square $(x-1)^2$ is zero at $x=1$ . That input gives the turning point, called the vertex.
Step 2
Check that the vertex is a high point
A square can't be negative, so multiplying $(x-1)^2$ by $-2$ gives a term that is never positive: $-2(x-1)^2\le 0$ . That term can only lower the output from the constant.
Step 3
Read the greatest output
At $x=1$ , the squared term is zero, so the output is $7$ . The negative coefficient makes the vertex's output the maximum. Don't grid in $1$ : that's the input, not the value of $g(x)$ . The maximum value is $7$ . Grid in 7.

Question 698·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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