Question 187699This question is from textbook mathematical analysis
: If Y= f(x)= 5-x-3x^2
Find
a) the Y-intercept
b) the X-intercept
c) th vertex
With full details please
Thank you,,
This question is from textbook mathematical analysis
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! If Y= f(x)= 5-x-3x^2
Find
a) the Y-intercept
y = -3x^2 - x + 5
Set x = 0 and solve for y:
y = -3(0)^2 - 0 + 5
y = -0 - 0 + 5
y = 5
So, y-intercept is at (0, 5)
.
b) the X-intercept
Set y = 0 and solve for x:
y = -3x^2 - x + 5
0 = -3x^2 - x + 5
Since we can't factor, we must use the quadratic equation.
Doing so yields:
x = {-1.468, 1.135}
Note: details at the end
.
c) the vertex
.
vertex form:
y= a(x-h)^2+k
.
Starting with:
y = -3x^2 - x + 5
y = -3(x^2 + (1/3)x) + 5
y = -3(x^2 + (1/3)x + 1/36) + 5 + 1/13
y = -3(x + 1/6)^2 + 66/13
y = -3(x - (-1/6))^2 + 66/13
.
Therefore, vertex is at (-1/6, 66/13)
.
.
.
Details of solving the quadratic for part b follows:
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=61 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: -1.46837494598444, 1.13504161265111.
Here's your graph:
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