All about interpretation of quadratic equation graphs.
A) vertex = (-1, 0)
B) axis of symmetry is; x = -1
C) x-intercept = -1
D) y-intercept = 1
E) Function is minimum when is minimum when x = -1
F) The range of the function is a set of all real numbers.
G) Domain is a set of all real numbers [tex]\geq[/tex] 0
H) Graph is attached
We are given;
f(x) = x² + 2x + 1
This follows the general form of a quadratic equation which is;
y = ax² + bx + c
In the function, we can say that;
a = 1
b = 2
c = 1
Thus; x = -2/(2 × 1)
x = -1
To get the y-coordinate of the vertex, we will put -1 for x in the given function to get; y = (-1)² + 2(-1) + 1 = 0
Thus, vertex = (-1, 0)
Thus, axis of symmetry is; x = -1
c) x-intercept is the value of x when y is 0.
As seen under vertex coordinate, y = 0 when x = -1.
Thus, x-intercept = -1
d) y-intercept is the value of y when x is 0. Thus;
y = 0² + 2(0) + 1
y-intercept = 1
e) a is greater than 0 and it means that the parabola opens up and so the function will have a minimum value.
y will be minimum when x = -b/2a
Thus, y is minimum when x = -1
f) The domain is the set of values of x for which the function remains defined.
Generally, quadratic graphs extend infinitely with respect to the x-axis and so we can say any real number for x will work.
Thus, range is a set of all real numbers.
g) From the vertex, we saw that the minimum point on the y-axis is at y = 0. The range is a set of all possible output values. Thus, the range is the set of all real numbers greater than or equal to zero.
h) Find attached the graph
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