Answer:
down
vertex: (0.25, 4.25)
axis of symmetry : x = 0.25
y-intercept: (0.4)
x-intercept: (-0.781, 0) and ( 1.281, 0)
Step-by-step explanation:
If we have a quadratic function of the form
then the graph opens downward if a < 1.
The quadratic function we have is
Since a = -4 < 1, the graph of the function opens downward.
The x-coordinate of the vertex of the function is given by
which is also the x-axis of symmetry of the graph ( the axis of symmetry passes through the vertex.
Now in our case a = -4 and b = 2; therefore, the vertex is
the above is the x-coordinate of the vertex. The y-coordinate is found by putting x = 0.25 into our function. This gives
the above simplifies to give
Hence, the coordinates of the vertex are (0.25, 4.25).
The y-intercept is found by putting x = 0 into the function. This gives
Hence, the y-intercept is at (0,4).
The x-intercepts are the soltuions to
Using the quadratic formula, the solutions we get are
which simplifies to give
Meaning, the x-intercepts are (-0.781, 0) and ( 1.281, 0).
Hence, to summerise our answers
down
vertex: (0.25, 4.25)
axis of symmetry : x = 0.25
y-intercept: (0.4)
x-intercept: (-0.781, 0) and ( 1.281, 0)
The graph of the function is attached below.