Question

the graph of y=f(x) is shown. a. estimate the turning point of the graph

Answer 1

Answer:

a) The location of the turning point is approximately $V(x,y) = (-0.25, -2,1)$.

b) Roots are approximately $x_{1} \approx -1.3$ and $x_{2} \approx 0.8$.

c) $f(1.5) \approx 4$

Step-by-step explanation:

a) The figure presents the graphic of a parabola, that is, a second order polynomial, with an absolute minimum (vertex). The turning point of the graphic, that is, the point in which behavior of the curve changes, is the vertex. Hence, the location of the turning point is approximately $V(x,y) = (-0.25, -2,1)$

b) According to the Quadratic Formula, second-order polynomials can have either two real roots or two conjugated complex roots. In this case, we have two real roots. A root corresponds with the point of the curve that passes through x-axis. In this case, roots are approximately $x_{1} \approx -1.3$ and $x_{2} \approx 0.8$.

c) $f(1.5)$ is the function evaluated at $x = 1.5$, that is, the value on y-axis associated with $x = 1.5$. Lastly, we conclude that $f(1.5) \approx 4$.