How many solutions does the following system have? 2x- 4y = 11 -2x + 4y = -10
2 answers:
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Answer:
Part 1) The vertex is the point (1,-9)
Part 2) The equation of the axis of symmetry is x=1
Part 3) The y-intercept is the point (0,-8)
Part 4) The x-intercepts are (-2,0) and (4,0)
Part 5) The graph in the attached figure
Step-by-step explanation:
we have
This is a vertical parabola open upward
The vertex represent a minimum
Part 1) Find the vertex
The quadratic equation is written in vertex form
where
(h,k) is the vertex of the parabola
so
The vertex is the point (1,-9)
Part 2) Find the axis of symmetry
The equation of the axis of symmetry of a vertical parabola is equal the the x-coordinate of the vertex
so
The equation of the axis of symmetry is
Part 3) Find the y-intercept
we know that
The y-intercept is the value of the function when the value of x is equal to zero
so
For x=0
therefore
The y-intercept is the point (0,-8)
Part 4) Find the x-intercepts
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
so
For h(x)=0
solve for x
square root both sides
therefore
The x-intercepts are (-2,0) and (4,0)
Part 5) Plot the graph of the quadratic function
Plot the following points to graph the function
vertex (1,-9)
axis of symmetry x=1
y-intercept (0,-8)
x-intercepts (-2,0) and (4,0)
The graph in the attached figure
