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Identifying Graphs of Quadratic Equations

7.12.5 Identifying Graphs of Quadratic Equations

7.12.5 • Identifying Graphs of Quadratic Equations

Cool Down

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

f(x)=x2−4f(x)=x2−4

g(x)=1−x2g(x)=1−x2

h(x)=x2+4h(x)=x2+4

Graph of three parabolas on a coordinate plane. The x-axis extends from negative 5 to 5 with a scale of 1. The y-axis extends from negative 8 to 10 with a scale of 2. The green parabola is labeled function A. The blue parabola is labeled function B. The black parabola is labeled function C.
1.

Which graph represents the equation f(x)=x2−4f(x)=x2−4?

Blue Graph B because the yy-intercept is (0,−4)(0,−4) and the graph opens upward.

2.

Which graph represents the equation g(x)=1−x2g(x)=1−x2?

Black Graph C because the yy-intercept is (0,1)(0,1) and the graph opens downward.

3.

Which graph represents the equation h(x)=x2+4h(x)=x2+4?

Green Graph A because the yy-intercept is (0,4)(0,4) and the graph opens upward.

4.

Which part of the equation tells us that Graph C opens downward?

Compare your answer:

y=1−x2y=1−x2 is the equation. The negative coefficient of x2x2 makes the graph open downward.