The system of equations graphed below has solutions . If the system is
between and , then the value of must be:

Ask by Moreno Lambert. in Canada

Mar 27,2025

Question

The system of equations graphed below has solutions $$ x= \pm 2 $$. If the system is between $$ y=x^{2} $$ and $$ y=-x^{2}+k $$, then the value of $$ k $$ must be:

UpStudy AI · Accepted Answer

To find the value of $$ k $$, we set the two equations equal to each other:

$$
x^2 = -x^2 + k
$$

Adding $$ x^2 $$ to both sides gives:

$$
2x^2 = k
$$

The problem states that the solutions for $$ x $$ are $$ x=\pm 2 $$. Substitute $$ x=2 $$ into the equation:

$$
2(2^2) = k \quad \Rightarrow \quad 2(4) = k \quad \Rightarrow \quad k=8
$$

Thus, the value of $$ k $$ must be $$ 8 $$.
$$ k = 8 $$

The system of equations graphed below has solutions . If the system is
between and , then the value of must be:

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The system of equations graphed below has solutions . If the system is between and , then the value of must be: