What is the y value of the vertex

y value = 49

Step-by-step explanation:

You are going to be completing the square

y = - x^2 - 10x + 24           Take a minus outside the brackets for the first 2 terms.

y = - (x^2 + 10x) + 24

Take 1/2 the linear term (1/2 10 and square it. Put that value inside the brackets. 1/2* 10 =5; 5^2 = 25

y = - (x^2 + 10x + 25) + 24

Add 25 outside the brackets.

y = -(x^2 + 10x + 25) + 24 + 25. You should stop here and consider why you are adding 25 outside the brackets. It is because there is a - sign in front of the trinomial and what is inside the brackets is really - 25 when the brackets are removed. Therefore to balance that, you add 25.

Now complete the square.

y = - ( x + 5)^2 + 49

The value you seek is 49.

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I'll confirm this with a graph.

The slope of the point given is .

To find this, you use the formula (y2 - y1)/(x2 - x1). Filling in all the values leaves you with (7 - (-2))/(4 - 3). When subtracting a negative from something you simply add it to the value. So the final equation says:

(7 + 2)/(4 - 3).

Now, you solve. 7 + 2 = 9 and 4 - 3 = 1. So your slope is 9/1 or simply just 9. Heres an image to show my work for this problem. I hope this helps!