Let's consider the equation of parabola, y = a·(x - α)·(x - β)
where α, β are the x-intercepts.
From the given graph, the y-intercept is (0, -3).
From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.
So the equation of parabola would be now, y = a·(x + 1)·(x - 3)
We can plug the y-intercept (0, -3) in the equation to find value of 'a'.
-3 = a·(0+1)·(0-3)
-3 = -3a
a = 1
So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3
Comparing it with y = ax² + bx + c
The x-coordinate of vertex would be,
the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.
Hence, vertex would be (1, -4).
Answer:
Step-by-step explanation:
The formula for area of a rectange is lw, where l is length and w is width. Since x-4 and 5x+2 are the sides, we can multiply them together to give us the area. We do (x-4)(5x+2). We use the FOIL method (First Outside Inside Last) and get 5x^2-18x-8.
Answer:
A
Step-by-step explanation:
The velocity of a moving body is given by the equation:
Is the velocity is <em>positive </em>(v>0), then our object will be moving <em>forwards</em>.
And if the velocity is negative (v<0), then our object will be moving <em>backwards</em>.
We want to find between which interval(s) is the object moving backwards. Hence, the second condition. Therefore:
By substitution:
Solve. To do so, we can first solve for <em>t</em> and then test values. By factoring:
Zero Product Property:
Now, by testing values for t<1, 1<t<4, and t>4, we see that:
So, the (only) interval for which <em>v</em> is <0 is the second interval: 1<t<4.
Hence, our answer is A.
Answer:
Step-by-step explanation: