Find the coordinates by solving and graphing the equation : -x^2-x+30=0
Diiscriminant :
D = b ^ 2 - 4 a c
in this case :
a = - 1
b = - 1
c = 30
D = ( - 1 ) ^ 2 - 4 * ( - 1 ) * 30
D = 1 + 4 * 30 = 1 + 120 = 121
x1/2 = - b + OR - sqrt ( b ^ 2 - 4 a c ) / 2a
in this case :
x1 = - b + sqrt( b ^ 2 - 4 a c ) / 2a
x1 = [ - ( - 1 ) + sqrt ( 121 ) ] / [ 2 * ( - 1 ) ]
x1 = ( 1 + 11 ) / ( - 2 )
x1 = 12 / - 2
x1 = - 6
x2 = - b - sqrt( b ^ 2 - 4 a c ) / 2a
x2 = [ - ( - 1 ) - sqrt ( 121 ) ] / [ 2 * ( - 1 ) ]
x2 = ( 1 - 11 ) / ( - 2 )
x2 = -10 / - 2
x2 = 5
If you want to see graph in google type:
functions graphs online
When you see results click on :
rechneronline.de/function-graphs/
When page be open in blue rectangle type :
- x ^ 2 - x + 30
Then set :
Range x-axis from - 10 to 10
Range x-axis from - 15 to 35
and click option : Draw
x1/2 = [ - b + OR - sqrt ( b ^ 2 - 4 a c ) ] / 2a
To find the coordinates by solving and graphing the equation -x^2 - x + 30 = 0, we can follow these steps:
Step 1: Rewrite the equation in the form of ax^2 + bx + c = 0. In this case, -x^2 - x + 30 = 0 is already in this form.
Step 2: Identify the values of a, b, and c. In our equation, a = -1, b = -1, and c = 30.
Step 3: Use the quadratic formula to find the roots (or x-intercepts) of the equation. The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in our values, we have:
x = (-(-1) ± √((-1)^2 - 4(-1)(30))) / (2(-1))
x = (1 ± √(1 + 120)) / -2
x = (1 ± √121) / -2
x = (1 ± 11) / -2
So the two possible roots are:
x1 = (1 + 11) / -2 = -12/2 = -6
x2 = (1 - 11) / -2 = -10/ -2 = 5
Step 4: The coordinates of the points can be found using the x-values obtained in the previous step. Since these are x-intercepts, the y-coordinate is 0 for both points.
So the coordinates of the points are:
Point 1: (-6, 0)
Point 2: (5, 0)
Step 5: Graph the equation on a coordinate plane. Plot the two points (-6, 0) and (5, 0) on the x-axis. Then, draw a smooth curve passing through these points to represent the graph of the equation -x^2 - x + 30 = 0.