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Question 948333: given f(x)=2x^2+5x+3.
a) the y-intercept
b) the x-intercept, if any
c) the vertex
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! f(x)=2x^2+5x+3
Section A: Y-intercept
The y-intercept is the y value(s) where x=0
In this case:
 ANSWER A The y-intercept is (0,3)
Section B: X-intercept
The graph intercepts the x axis when the y value is 0, so:
| 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=1 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: -1, -1.5.
Here's your graph:
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Thus the x-intercepts are at -1 and -1.5 or
ANSWER B: X=intercepts are at (-1,0) and (-1.5,0).
Section C: Vertex
Given equation of form:
the axis of symmetry (x value of vertex) is given by:
In this case:
 =
Use this x value in the equation to find y value of vertex
 = ANSWER C: The vertex is at (-5/4,-1/8)
This graph shows the vertex more clearly, with x- and y- intercepts:
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