(i)Write down the coordinates of the vertex (minimum point) of the curve with equation y=x^2+10x+19.
(ii) write down the equation of the line of symmetry of the curve y=x^2+10x+19.
Please show your working out if possible.
Thank You :)
(ii) write down the equation of the line of symmetry of the curve y=x^2+10x+19.
Please show your working out if possible.
Thank You :)
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I am going to do it in the calculus way.
If you have not learnt calculus, you might want to do it in another way.
The equation y=x^2+10x+19 is a parabola.
To find the coordinates of the vertex, first take the derivative of the equation.
Which is y'=2x+10
If you don't understand this, you can think of it in this way.
Instead of y'=2x+10, you can think of this -----> slope=2x+10
At the vertex, the slope is 0....Therefore you can put it in this way---> 0=2x+10
Then you solve for x. Once you have x, put the x value back to y=x^2+10x+19 to solve for y.
So now, you have both x and y, and that will be the coordinates.
I will leave the solving part to you.
As for part 2, the line of symmetry is basically a straight line that divides the parabola into 2 equal parts. So the line will have the equation x =
So the answer is x =
If you have not learnt calculus, you might want to do it in another way.
The equation y=x^2+10x+19 is a parabola.
To find the coordinates of the vertex, first take the derivative of the equation.
Which is y'=2x+10
If you don't understand this, you can think of it in this way.
Instead of y'=2x+10, you can think of this -----> slope=2x+10
At the vertex, the slope is 0....Therefore you can put it in this way---> 0=2x+10
Then you solve for x. Once you have x, put the x value back to y=x^2+10x+19 to solve for y.
So now, you have both x and y, and that will be the coordinates.
I will leave the solving part to you.
As for part 2, the line of symmetry is basically a straight line that divides the parabola into 2 equal parts. So the line will have the equation x =
So the answer is x =