SOLUTION: Without drawing the graph determine how many x- intercepts the parabola has and whether its vertex lies above or below or on the x axis Show your work
y = x^2 - 5x + 6
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Question 203134: Without drawing the graph determine how many x- intercepts the parabola has and whether its vertex lies above or below or on the x axis Show your work
y = x^2 - 5x + 6
Found 2 solutions by jsmallt9, jojo14344:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
X-intercepts are where a a graph intersects the x-axis. In other words, x-intercepts are x-values which make the function value 0. So to find x-intercepts we need to find the x-value(s) where f(x) = 0.
So finding the x-intercepts of your function means solving:
Factoring this we get:
The only way for a product to be zero is if one of the factors is zero. So the solution to is: or . The solutions to these are: x = 2 or x = 3.
There are two x-intercepts: (2, 0) and (3, 0)
As for where the vertex is located, think about parabolas in general. In general the possibilities are:- The parabola is completely above the x-axis. These parabolas will have no x-intercepts and the leading coefficient is positive.
- The parabola is completely below the x-axis. These parabolas will have no x-intercepts and the leading coefficient is negative.
- Part of the parabola is above the x-axis and part of it is below the x-axis. These parabolas have 2 x-intercepts. If the leading coefficient is positive the vertex will be below the x-axis. If the leading coefficient is negative, the vertex will be above the x-axis.
- Parabolas whose vertex is not above or below but on the x-axis. These parabolas will have just one x-intercept, the vertex.
Our parabola has 2 x-intercepts and its leading coefficient is 1 (which is positive). So our vertex is below the x-axis.
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Given: , where}
Finding for X-intercepts via Quadratic:
, a perfect square
&
X-intercepts --> (3,0) & (2,0) Answer
For the vertex:
---> substitute to the eqn,
The vertex: (5/2,-1/4) or (2.5,-.25) ---> Lies below the X - axis being the Y-Intercept is negative (-).
To clearly demonstrate this, we see the graph
Thank you,
Jojo
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