Question

Instructions to use the graph calculator to approximate the zeros and vertex of the following quadratic functions. round to one decimal place, if necessary. fill in the solution least the greatest (left to write)

Answer 1

Given:

a quadratic function is given as y = x² - 8x + 3

Find:

we have to find the vertex and zeros of the given quadratic function.

Explanation:

The graph of the given function is shown below

From the above graph, it is observed that the vertex of the quadratic function is (4, -13).

Now, we will find the solution of the quadratic function as following

to find the solution, equate y = 0

i.e. x² - 8x + 3 = 0

$\begin{gathered} x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(3)}}{2(1)} \\ x=\frac{8\pm\sqrt{64-12}}{2} \\ x=\frac{8\pm\sqrt{52}}{2} \\ x=\frac{8\pm2\sqrt{13}}{2} \\ x=4+\sqrt{13},\text{ 4 -}\sqrt{13} \\ x=7.6,\text{ 0.4} \end{gathered}$

Therefore, the solutions are 0.4 and 7.6