Question

the x - intercepts of the graph of the quadratic function. then match the function with its graph.

( y = x ^ { 2 } - 10 x + 24 )

the x - intercepts are (use a comma to separate answers as needed.)

choose the correct graph below. each graph is shown in a ( - 10,10,1 ) by ( - 10,10,1 ) viewing rectangle.

Explanation:

Step1: Find the x - intercepts

To find the x - intercepts, set \(y = 0\). So we have the equation \(x^{2}-10x + 24=0\).
We can factor the quadratic equation. We need to find two numbers that multiply to \(24\) and add up to \(- 10\). The numbers are \(-4\) and \(-6\).
So, \(x^{2}-10x + 24=(x - 4)(x - 6)=0\).
Using the zero - product property \(a\times b = 0\) implies \(a = 0\) or \(b = 0\).
If \(x-4=0\), then \(x = 4\); if \(x - 6=0\), then \(x=6\).

Answer:

The x - intercepts are \(4,6\).