Chapter 9.5, Problem 32E

To determine

To find the number of $x$ -intercepts of the Quadratic equation.

Answer to Problem 32E

The number of $x$ -intercepts will be one.

Explanation of Solution

Given:

Equation:

  $y=4x^2+4x+1$

Formula used:

Discriminant formula.

  $D=b^2-4ac$

Calculation:

On comparing the equation with $a{x}^2+bx+c$

  $a=4,b=4,c=1$

Finding the value of $D$

  $D=b^2-4ac$

Substituting the values,

  $D={(4)}^2-4(4)(1)$

Opening brackets,

  $D=16-16$

So,

  $D=0$

Therefore,the number of $x$ -intercepts will be one.