Chapter 5 Polynomials and Polynomial Functions - 5.4 Factor and Solve Polynomial Equations - 5.4 Exercises - Mixed Review - Page 359: 67

See the graph

Given: $y=\frac{1}{2}x^2+4x+5$ Find the x-coordinate: $x=-\frac{b}{2a}=-\frac{4}{2.\frac{1}{2}}=-4$ Substitute for x to find y: $y=\frac{1}{2}(-4)^2+4(-4)+5=-3$ Hence, the vertex is $(-4,-3)$ The axis of symmetry is $x=-4$ Find some other points: $x=-6 \rightarrow y=-1$ $x=-5 \rightarrow y=-\frac{5}{2}$ $x=-3 \rightarrow y=-\frac{5}{2}$ $x=-2 \rightarrow y=-1$