The slope formula is y₁-y₂/x₁-x₂ so all we need is 2 points and the ones provided are -4, 3 and -2, -1 so all we do is plug them in to get 3--1/-4-2 which equals to 4/-6 which is -2/3
Step-by-step explanation: The slope of a line refers to its direction and steepness. The slope can be expressed as a fraction that is commonly refered to as rise over run. In order to find the slope of a line, you need to find two coordinates on the line and use the "rise over run" method. The numerator (rise) is how many units up or down while the denominator (run) is how many units left or right. There are two given points on this specific line. To get from one to the other, you must go down 4 units and to the right 2 units; therefore, the slope, or rise over run, is -4/2. This can be simplified to -2/1, which can be simplified even further to just -2.
a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.
b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.
c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.
d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.
e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.
