Here are graphs that represent three quadratic functions, defined by:

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f(x) = x^{2}-2

g(x) = 2 - x^{2}

h(x) = x^{2} + 3

  1. Match each equation to a graph that represents it. Explain how you know.
  2. Write down the equation that can be represented by Graph C. Which part of the equation tells us that the graph opens downward?

Sangeetha Pulapaka


f(x) is represented by graph B.

g(x) is represented by graph C.

h(x) is represented by graph A.

A quadratic equation is either in the form  ax^{2} + bx + c or f(x) = a(x-h)^{2} +k. This is the vertex form where (h, k) is the vertex, or the highest or the lowest point of the graph

If  a \neq 0. If a \lt 0 the graph opens up and if a \lt 0 the graph opens down.

f(x) = x^{2}-2 is in the vertex form. Since a = 1, this shows that the graph opens up and the vertex is at (0,-2). The graph B represents this quadratic equation.

g(x) = 2 - x^{2}, tells that a = -1, so the graph opens downward and the vertex is at (0,2). Graph C represents this graph.

h(x) = x^{2} + 3, tells us that a= 1 so our graph opens upward and the vertex is at (0,3). Graph A represents this graph.


As explained above, the equation g(x) = 2-x^{2} represents graph C. The negative sign before x^{2} or -x^{2} says that the value of a is negative and since a\lt 0, the graph opens downward.