Question 877·Easy·Math

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The function $g$ is defined by $g(x)=2x^2-3x+4$ . What is the value of $g(-1)$ ?

A given input in function notation tells you to evaluate: replace every $x$ in the rule with that input. Put a negative input in parentheses so you square the whole number and keep the signs straight. In Desmos, define the function, then type the requested value. The tempting slip is to treat the square of a negative number as negative.

Hints

Hint 1
In function notation, $g(a)$ means the output when the input is $a$ . Replace every $x$ in the rule with the input inside $g(-1)$ . How many places need replacing?
Hint 2
Parentheses make the whole negative input the base of the square: $(-1)^2$ is positive. A negative times a negative is positive too. What signs will the two variable terms have?

Step-by-step

Substitute, then evaluate in Desmos
Step 1
Put the input into the rule
$g(-1)$ means use $-1$ in both places where the rule has $x$ . Put the whole negative input in parentheses each time you replace $x$ . So
$g(-1)=2(-1)^2-3(-1)+4.$
Step 2
Check the squared term
Squaring means multiplying a number by itself. The whole $-1$ is squared, so
$(-1)^2=1.$
Step 3
Check the other sign
The term $-3x$ also uses $x=-1$ . Multiplying two negatives gives a positive:
$-3(-1)=3.$
Step 4
Read the output in Desmos
Type $g(x)=2x^2-3x+4$ , then type $g(-1)$ on the next line. Desmos shows $9$ : the squared term contributes $2$ , the other variable term contributes $3$ , and the constant contributes $4$ . So the value of $g(-1)$ is $9$ . Choice D.

Question 877·Easy·Math

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

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