Chapter 4.1, Problem 63HP

a.

To determine

Find the value of $a,b,candd$ .

Answer to Problem 63HP

  $a=22,b=26c=\pm 6d=0,2$

Explanation of Solution

Given information:

The table represents points on the graph of a quadratic function.

  $\begin{array}{cccccccccc}x& -20& c& -5& -1& d-1& 5& 7& 15& 14-c\\ y& -377& -13& -2& 22& a& a-24& -b& -202& -377\end{array}$

Calculation:

Consider the given table and graph the known values given in table,

  

According to the graph, the value $-13\text{}\text{}aty-axis$ correspond to the points $\pm 6$ at $x-axis$ but in the table $-13$ corresponds to $c$ .

Therefore $c=\pm 6$

Similarly in graph $atx=5,y=-2$ in table $x=5,y=a-24$

So,

  $\begin{array}{l}-2=a-24\\ a=22\end{array}$

Similarly in graph $x=5,y=-26$ in table $x=7,y=-b$

  $\begin{array}{l}-b=-26\\ b=26\end{array}$

  $\begin{array}{l}now,\\ d-1=\pm 1\\ d=0,2\end{array}$

Hence, $a=22,b=26c=\pm 6d=0,2$ .

b.

To determine

Find the $x-coordinate$ of the vertex.

Answer to Problem 63HP

  $0$

Explanation of Solution

Given information:

The table represents points on the graph of a quadratic function.

  $\begin{array}{cccccccccc}x& -20& c& -5& -1& d-1& 5& 7& 15& 14-c\\ y& -377& -13& -2& 22& a& a-24& -b& -202& -377\end{array}$

Calculation:

Consider the graph,

  

  $x-coordinate$ of the vertex is $0$ .

c.

To determine

Verify the function for maximum and minimum.

Answer to Problem 63HP

Maximum.

Explanation of Solution

Given information:

The table represents points on the graph of a quadratic function.

  $\begin{array}{cccccccccc}x& -20& c& -5& -1& d-1& 5& 7& 15& 14-c\\ y& -377& -13& -2& 22& a& a-24& -b& -202& -377\end{array}$

Calculation:

Consider the graph,

  

As the open downward , then the leading coofficient of the parabola is nagetive, then parabola has maximum value,

Hence, the quadratic function has maximum.