how to i graph the inequality :
y<x squared - 3x + 15
whats my x and whats my y ? should i factor ?
To graph the inequality, graph :
Y= x^2 - 3x + 15 = 0,
Step 1. Find the coordinates (h,k) of
the vertex:
h = Xv = -b/2a = 3/2 = 1.5,
Substitute 1.5 for x in the guad. Eq:
k = Yv = (1.5^2) - 3*1.5 + 15 = 12.75,
V(1.5 , 12.75),
Step 2. Select values of x above and
below h(Xv) and cal. the corresponding value of y:
(-1 , 19), (0 , 15), (1 , 13), (1.5 , 12.75), (2 , 13), (3 , 15).
The parabola does not cross the x-axis.
Therefore, there are no real solutions.
But we have 2 imaginary solutions(roots) which can be cal. using the
quadratic formula.
Take the corresponding number of every letter and the alphabet and add, but this is impossibru so I'm out, PEACE
good mornin
To graph the inequality y < x^2 - 3x + 15, you can follow these steps:
1. Start by graphing the equation y = x^2 - 3x + 15. This will help you understand the shape of the parabola.
2. To graph the equation, you can find the vertex of the parabola using the formula x = -b/2a. For this equation, the coefficients are a = 1, b = -3, and c = 15.
Use the formula to find the x-coordinate of the vertex:
x = -(-3) / 2(1) = 3/2 = 1.5
Then substitute the x-coordinate into the equation to find the y-coordinate:
y = (1.5)^2 - 3(1.5) + 15 = 10.25
So, the vertex of the parabola is (1.5, 10.25).
3. Plot the vertex on your graph.
4. Next, find the x-intercepts (if any) by setting y = 0 and solving for x. If this parabola does not intersect the x-axis, skip this step.
Set x^2 - 3x + 15 = 0 and solve using factoring or the quadratic formula. If the equation does not factor easily, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
Let's solve it using the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(1)(15))) / 2(1)
x = (3 ± √(9 - 60)) / 2
x = (3 ± √(-51)) / 2
Since we can't take the square root of a negative number, there are no x-intercepts. But keep in mind that this might not always be the case.
5. Now, you can determine whether the shading should be above or below the graph. Since the inequality is y < x^2 - 3x + 15, the shading should be below the curve.
6. Finally, draw the graph of the parabola from step 1 and shade below it to represent the inequality y < x^2 - 3x + 15.
Remember that graphing an inequality involves the same steps as graphing an equation, but with a few additional considerations for shading the region that satisfies the inequality.