Question

What is the graph 4=y2

Answer 1

Answer:

• Number line with marks on y = 2 and y = -2. See the first graph attached.

Explanation:

• 4 = y² is an equation that yields two values of y.

Then, its graph consists of two points on the number line;

         $4=y^2\\\\y^2=4\\\\y=\pm\sqrt{4} \\\\y=\pm2\\\\y_1=2\\\\y_2=-2$

That is, the graph istwo points that show the solutions, one point on the mark y = 2 and the other on the mark y = -2.

This is a one dimensional graph: just two points on the number line.

See the first graph attahed.

I will also talk you about the function 4x = y², just in case the question is mssing the variable x.

The graph of 4x = y² is a horizontal parabola, i.e. it symmetry axis is parallel to the x-axis.

The standard form of the equation of a horizontal  parabola is:

          $(y-k)^2=4p(x-h)$

With p ≠ 0.

The point with coordinates (h,k) is the vertex.

The point with coordinates (h + p, k) is the focus.

The line x = h - p is the directrix.

The axis of symmetry is the line y = k.

Positive values of p (p > 0) means the parabola opens to the right, and negative values of p (p < 0), means the parabola opens to the left.

4x = y² means:

• h = 0, k = 0, 4p = 4 ⇒ p = 1.

Then:

• vertex (0,0)
• focus (0,0)
• directrix: line x  = 0 - 1 = - 1
• axis of symmetry: line y = 0
• it opens to the right.

With that, you can understand the second graph attached.