y=x^2+4

Frequently Asked Questions

• Find the vertex of \(y=x^2+4\)

  

  $$\left(0,4\right)$$

• Find the axis of symmetry of \(y=x^2+4\)

  

  $$x=0$$

• Evaluate the derivative of \(y=x^2+4\)

  

  $$y^{\prime }=2x$$

• Find the domain of \(y=x^2+4\)

  

  $$x\in \mathbb{R}$$

• $$\text{Find the }x\text{-intercept/zero}$$ of \(y=x^2+4\)

  

  $$\text{No x-intercept}$$

• Find the y-intercept of \(y=x^2+4\)

  

  $$y=4$$

• Find the critical numbers of \(y=x^2+4\)

  

  $$x=0$$

• Find the local extrema of \(y=x^2+4\)

  

  $$\begin{array}{rl}& \text{The local minimum is }4\text{ at }x=0\end{array}$$

• Find the increasing or decreasing interval of \(y=x^2+4\)

  

  $$\begin{array}{rl}& \text{The increasing interval is}x\ge 0\\ & \text{The decreasing interval is}x\le 0\end{array}$$

• Find the range of \(y=x^2+4\)

  

  $$y\ge 4$$

• Find the vertical asymptotes of \(y=x^2+4\)

  

  $$\text{No vertical asymptotes}$$

• Find the horizontal asymptotes of \(y=x^2+4\)

  

  $$\text{No horizontal asymptotes}$$

• Find the oblique asymptotes of \(y=x^2+4\)

  

  $$\text{No oblique asymptotes}$$

• Determine if even, odd or neither of \(y=x^2+4\)

  

  $$\text{Even}$$

• Find the stationary points of \(y=x^2+4\)

  

  $$\left(0,4\right)$$

• Find the inflection points of \(y=x^2+4\)

  

  $$\text{No inflection points}$$

• Testing for symmetry about the origin of \(y=x^2+4\)

  

  $$\text{Not symmetry with respect to the origin}$$

• Testing for symmetry about the x-axis of \(y=x^2+4\)

  

  $$\text{Not symmetry with respect to the x-axis}$$

• Testing for symmetry about the y-axis of \(y=x^2+4\)

  

  $$\text{Symmetry with respect to the y-axis}$$

• Find the standard equation of the parabola of \(y=x^2+4\)

  

  $$x^2=y-4$$

• Find the vertex of the parabola of \(y=x^2+4\)

  

  $$\left(0,4\right)$$

• Find the focus of the parabola of \(y=x^2+4\)

  

  $$F=\left(0,\frac{17}{4}\right)$$

• Find the directrix of the parabola of \(y=x^2+4\)

  

  $$y=\frac{15}{4}$$

• $$\text{Solve for }x$$ of \(y=x^2+4\)

  

  $$\begin{array}{rl}& x=\sqrt{y-4}\\ & x=-\sqrt{y-4}\end{array}$$

• Rewrite in polar form of \(y=x^2+4\)

  

  $$\begin{array}{rl}& r=\frac{\sin \left(\theta \right)-\sqrt{17{\sin }^2\left(\theta \right)-16}}{2{\cos }^2\left(\theta \right)}\\ & r=\frac{\sin \left(\theta \right)+\sqrt{17{\sin }^2\left(\theta \right)-16}}{2{\cos }^2\left(\theta \right)}\end{array}$$