Question

How many times does the graph of$\mathit{y}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{x}\mathbf{+}\mathbf{10}$cross the $\mathit{x}$-axis?

Short answer

The graph of$y=x^2-4x+10$ will cross the $x$-axis2 times.

Step-by-step solution

Step 1. State the concept of ‘zeroes of polynomial’.

All the values of the variable in a given polynomial which makes the polynomial zero are called as the zeroes of polynomial.

These zeroes will give the number of times the graph crosses the $x$-axis.

Step 2. Calculate the number of zeroes of the given equation.

The equation $y=x^2-4x+10$is a quadratic equation and its degree is 2.

The number of zeroes of a polynomial is equal to the highest degree of the polynomial.

Therefore, the equation $y=x^2-4x+10$has two zeroes.

Step 3. State the conclusion.

Since the equation$y=x^2-4x+10$has two zeroes, it will cross x-axis twice.