To plot a quadratic graph you need the y intercept, the X intercepts(the roots) and the minimum/ maximum.

For the first question:

Y intercepts is -7, so u have the point(0,-7)

U can complete the square for the max/min -x^2-4x-7=y -1(x^2+4x)-7=y -1((X+2)^2-4)-7=y -1(X+2)^2+4-7=y -1(X+2)^2-3=y It's a negative quadratic so it's a maximum U need to make the number in the bracket = 0, so when X =-2, y = -3
So maximum point is (-2,-3)

To find the roots u make the equation equal to 0 and find what X equals. U can do this using quadratic formula, factorising or completing the square. -1(X+2)^2-3=0 -1(X+2)²⁼³ (X+2)²⁼ -3 X+2= √-3 You can't square root a negative number so there are no roots, meaning the line will not touch the X axis.

Now u just need to plot the y int and maximum on ur graph The graph