Q8. - Algebra 1

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?

Step-by-Step Solution

Answer

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

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.