Chapter 1.4, Problem 46E

Solution

To find: The zeros of the function $y=16x^2-2x-5$ by writing in intercept form.

  $x=-\frac{1}{2}$ , $x=\frac{5}{8}$ .

Given information:

The function, $y=16x^2-2x-5$ .

Concept used:

The intercept form of a quadratic function is given as $y=\left(x-a\right)\left(x-b\right)$ , where $a$ and $b$ are zeros of the function.

Calculation:

Rewrite the function in intercept form as follows:

  $\begin{array}{c}y=16x^2-2x-5\\ =\left(16x^2+8x\right)+\left(-10x-5\right)\\ =8x\left(2x+1\right)-5\left(2x+1\right)\\ =\left(2x+1\right)\left(8x-5\right)\end{array}$

The intercept of the function are the points where the factors $2x+1=0$ and $8x-5=0$ .

Solve the two equations to find the intercepts.

  $\begin{array}{c}2x+1=0\\ x=-\frac{1}{2}\end{array}$

And,

  $\begin{array}{c}8x-5=0\\ x=\frac{5}{8}\end{array}$

Conclusion:

The zeros of the function are $x=-\frac{1}{2}$ and $x=\frac{5}{8}$ .