graph the solution to the following system of inequalities.
$$
\left\{\begin{array} { l } { y \geq x ^ { 2 } - 1 } \\ { x ^ { 2 } + y ^ { 2 }

Question

graph the solution to the following system of inequalities.
$$
\left\{\begin{array} { l } { y \geq x ^ { 2 } - 1 } \\ { x ^ { 2 } + y ^ { 2 } < 25 } \end{array}\
ight.
$$

Accepted Answer

# Explanation:
## Step1: Graph $ y\geq x^{2}-1 $
The parabola $ y = x^{2}-1 $ has vertex $(0,-1)$ and opens upward. Since $ y\geq x^{2}-1 $, shade above (including the parabola).
## Step2: Graph $ x^{2}+y^{2}<25 $
The equation $ x^{2}+y^{2}=25 $ is a circle with center $(0,0)$ and radius $ r = 5 $. Since $ x^{2}+y^{2}<25 $, shade the interior (not including the circle).
## Step3: Find the intersection
The solution is the region that is shaded for both inequalities.

# Answer:
Graph the parabola $ y=x^{2}-1 $ (solid line, shade above), graph the circle $ x^{2}+y^{2}=25 $ (dashed line, shade inside), and the overlapping region is the solution.

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QUESTION IMAGE

Question

Explanation:

Step1: Graph \( y\geq x^{2}-1 \)

Step2: Graph \( x^{2}+y^{2}<25 \)

Step3: Find the intersection

Answer: