Question 16·SAT Desmos Regression Practice·Advanced Math

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The graph of the function $q$ , defined by $q(x)=a(x-1)^2+2$ , is shown. What is the value of $a$ ?

Your answer

The equation is in vertex form, which already fixes the parabola’s turning point but leaves $a$ unknown. Look for a different point on the graph: put its $x$ -coordinate into the function and set the result equal to its $y$ -coordinate. Enter that equation as a Desmos regression to find $a$ . Don’t mistake the point’s output for the coefficient.

Hints

Hint 1
The vertex is the parabola’s turning point. At the vertex input, the squared part of this equation is $0$ no matter what $a$ is. Which labeled point gives you information about $a$ ?
Hint 2
A point $(u,v)$ on a graph means $q(u)=v$ : the first coordinate is the input, and the second is the output. Use the labeled point to write an equation with $a$ .

Step-by-step

Use the labeled point
Step 1
Read a useful point from the graph
The labeled point $(3,10)$ is on the curve, so $q(3)=10$ : input $3$ gives output $10$ . Use a point away from the vertex to find $a$ . At the vertex, the turning point $(1,2)$ , the squared part is $0$ for every $a$ .
Step 2
Turn the point into an equation
Put the point’s input $3$ in for $x$ in the given function. Its output must be $10$ , so:
$10=a(3-1)^2+2.$
Step 3
Find the coefficient in Desmos
Type $10\sim a(3-1)^2+2$ . The tilde $\sim$ tells Desmos to find the unknown $a$ rather than make a slider. Under PARAMETERS, Desmos shows $a=2$ . So the coefficient in $q(x)$ is $2$ . Grid in 2.

Question 16·SAT Desmos Regression Practice·Advanced Math

Strategy

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Step-by-step

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