Answer
$y=0$
Work Step by Step
1. The tangent line at x=a passes through the point (a, f(a))$\\$
(we must first find f(a)$\\$
2. It has slope m$=f^{\prime}(a)\\$
3. Its equation (point slope): $y-f(a)=f^{\prime}(a)(x-a)\\$
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1. $x=0, \ \ \ f(0)$=$(0)^{2}=0.\\$
The point on the graph is $(0,0).\\$
2. Slope. $\\$
$f^{\prime}(x)=$ (power rule)$ = 2x\\$
$m=f^{\prime}(0)=2(0)^{2}=0\\$
3. Equation.
The slope is 0, so the tangent is horizontal,
passing through the origin:
$y=0$
(the x-axis)
image enclosed: graph
