-b/2a = x value of turning point = -(10)/2(1) = -5 Plug -5 back into the quadratic to find y value f(-5) = (-5)^2+10(-5)+24 = -1 Turning Point = (-5,-1)
Bro thanks.. here is an easy way of doing it a=1 b=10 c=24 Step 1. p= -b/2a p=-(10)/2(a) p=-10/2 p=-5 Note: p is equals to the x coordinate . Step 2: q= 4(a) (c) - (b)²/ 4(a) q=4(1) (24) - (10)²/ 4(1) q= 96 - 100/ 4 q=-4/4 q= -1 (-5,-1) Note: q is equals to the y coordinate.
when we have a quadratic eqn with a negative coefficeint, does this still work as is or must we take the - sign in common and THEN carry the formula out?
A quadratic only has one turning point but for equations with two turning points you can use calculus. If the derivative = 0 and the second derivative does not = 0 then it is a turning point. If you find all the x values that make the first derivative 0, you can test them by plugging in to the second derivative to make sure the second derivative does not = 0. You can then plug in all the x values that passed the test into the original function to get the y coordinates of the turning points. I also think it is easier to use derivatives for quadratic functions to find turning points. You can super easily find the derivative in your head which would be 2x + 10. If you set it equal to 0, you get that the x coordinate is -5 and you plug that back in to the original function to get the y coordinate. You don't need to check the second derivative because there are no points of inflection on a quadratic.
When you change x² + 10x into (x + 5)², the x² and the 10x remain the same, but you end up with an additional product of 25, which must be negated by subtracting 25.
basically what he did was +(5)^2 which went in the bracket with x making it (x+5)^2 then -(5)^2 which gave us -25. If u want to know the reason behind this, he used the completing square method. I recommend watching a few videos on it as it is really easy to learn and helps a lot with problems like these and is the easiest method to figuring out equations of circles.
Here is something for you a=1 b=10 c=24 Step 1. p= -b/2a p=-(10)/2(a) p=-10/2 p=-5 Note: p is equals to the x coordinate . Step 2: q= 4(a) (c) - (b)²/ 4(a) q=4(1) (24) - (10)²/ 4(1) q= 96 - 100/ 4 q=-4/4 q= -1 (-5,-1) Note: q is equals to the y coordinate.
