Sketch the quadratic function f(x) = x2 + 4x + 3. Which key feature of the graph is given incorrectly?
2 answers:
Given quadratic function
Let us find vertex of the graph first.
x-coordinate of the vertex = -b/2a = -4/2(1) = -4/2 = -2.
y-coordinate of the vertex = (-2)^2+4(-2)+3 = 4-8+3 = -1.
Therefore, vertex is at (-2,-1).
The leading coefficient of quadratic function f(x)= x^2+4x+3 is 1.
And it's a positive number.
So, the parabola open up and it would have a minimum at it's vertex point.
Let us find some more points on the graph :
x=-3
(-3)^2 +4(-3) +3 = 9 -12 +3 =0
x=-1
(-1)^2 +4(-1) +3 = 1 -4 +3 = 0.
<em>From the graph, we can see vertex is at (-2,-1) and x-intercepts at (-1,0), (-3,0) and y-intercept at (0,3).</em>
Therefore, following is the key feature of the graph is given incorrectly:
<h2>B) y-intercept (0, 2) </h2>
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We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is . The graph of the function does not show a phase shift. We are asked to write the equation of our function.
We know that general form a cosine function is , where,
A = Amplitude,
= Period,
c = Horizontal shift,
d = Vertical shift.
The equation of parent cosine function is . Since function is reflected about x-axis, so our function will be
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Let us find the value of b.
Upon substituting our given values in general cosine function, we will get:
Therefore, our required function would be .