Question 823·Easy·Math

0 / 2000

$p(x)=2x^2-3$

Which table gives three values of $x$ and their corresponding values of $p(x)$ for the function $p$ ?

$x$	0	1	2
$p(x)$	-3	-1	6

$x$	0	1	2
$p(x)$	-1	-1	5

$x$	0	1	2
$p(x)$	-3	-2	5

$x$	0	1	2
$p(x)$	-3	-1	5

A function pairs each input with the output given by its rule. When a question asks which table matches a given function, define the rule once in Desmos and evaluate the listed inputs in order. Every input-output pair must agree. For a squared term, square the input before multiplying by the coefficient.

Hints

Hint 1
In function notation, $p(0)$ means put $0$ wherever the rule has $x$ . Find that output first. Which tables have the correct output paired with $x=0$ ?
Hint 2
One matching pair doesn't prove a table is right. Check each remaining input with the same rule. When you evaluate $p(2)$ , square the $2$ before multiplying by the coefficient.

Step-by-step

Evaluate each input in Desmos
Step 1
Find the output for zero
Type the given rule $p(x)=2x^2-3$ in Desmos, then type $p(0)$ . Desmos shows $-3$ . In function notation, $p(0)$ means the output when the input is $0$ , so a matching table needs $-3$ paired with $0$ .
Step 2
Find the output for one
Add $p(1)$ on the next Desmos line. It shows $-1$ , so the output paired with $1$ must be $-1$ . Don't stop because the first pair matched; a table must match at every input.
Step 3
Check the last pair and choose the table
Add $p(2)$ . Desmos shows $5$ . The rule squares $2$ before multiplying by $2$ , then subtracts $3$ . So the table must pair $0,1,2$ with $-3,-1,5$ , respectively. Choice D.

Question 823·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this