Zeroes

The point where the graph crosses the X Axis

When a standard form equation is given, it is possible to turn the equation into factored form. However this may not always work. To avoid this problem, it is better to just use the Quadratic Formula.

ax²+bx+c

turns to

-b+-√b²-4(a)(c)

2(a)

For Example

What are the x intercepts of the standard form equation 2x²+11x+9

Step 1: Put the standard equation into the the quadratic formula

-11+-√11²-4(2)(9)

2(2)

Step 2: Solve it further on

-11+-√11²-4(2)(9) -11+-√121-72 -11+-√49

2(2) 4 4

-11+-7 x=-1

4 x=-4.5

Question

What are the x intercepts of the standard form equation 3x²+16x+10?

Solution

Step 1: Put the standard equation into the the quadratic formula

-16+-√16²-4(3)(10)

2(3)

Step 2: Solve it further on

-16+-√16²-4(3)(10) -16+-√256-120 -16+-√136

2(3) 6 6

-16+-11.66 x=-0.7233

6 x=-4.61