00:03
We're going to find the x intercepts and vertex for this function and draw the graph.
00:08
So x intercepts are points that have a y coordinate of zero.
00:12
So let's go ahead and put zero in for y in the equation, and we'll solve for x.
00:17
We can use the zero product property and set each factor equal to zero and solve each equation.
00:24
So for the first equation, we'll add one to both sides and we get x equals one.
00:28
And for the second equation, we'll subtract seven from both sides and we get x equals negative seven.
00:32
So that means that our x intercepts are the points, 0 and negative 7 -0.
00:38
Now what about the vertex? we know based on the symmetry of a parabola that the vertex is halfway between the 2 x intercepts.
00:47
So what number is halfway between 1 and negative 7? that would be also known as the average.
00:53
So add them together and divide by 2 and you'll get negative 3.
00:56
That's the x coordinate of the vertex.
00:59
What about the y coordinate? what we can do is go back to our equation, put the x coordinate in for x, and solve for y.
01:08
So we end up with y equals negative 4 times 4...