Write the quadratic equation represented by the graph shown.
Let’s highlight some points on this graph. The graph goes through the origin zero, zero. It crosses at one, one and at negative one, one. There’s a point at two, four and negative two, four.
By this shape, we know that this is a parabola. And a parabola is the graph of 𝑦 equals 𝑥 squared. This parabola opens upward, which means it’s a positive 𝑥 squared. And because the graph goes through the origin, its 𝑦-intercept equals zero.
Let’s consider those points we looked at earlier. When 𝑥 equals one, one squared equals one. When 𝑥 equals negative one, negative one squared equals one. When 𝑥 equals two, we have two squared, which equals four. That’s point two, four. When 𝑥 equals negative two, 𝑦 equals four. That’s point negative two, four.
What we’re showing is that this graph is the quadratic equation 𝑦 equals 𝑥 squared. No transformations have occurred. It hasn’t been shifted up or down. It’s simply the graph of 𝑦 equals 𝑥 squared.