On a separate piece of paper, sketch the graph of the parabola f(x) = x2 + 4. On

Question

On a separate piece of paper, sketch the graph of the parabola f(x) = x2 + 4. On the same set of axes, plot the point (0. -4). Notice that there are two points on the parabola [of the form (Plus minus a. f(a)) ] at which the tangent lines to the parabola pass through (0, -4). Draw these two points and these two lines. The point with positive .x-coordinate that is on the parabola and has its tangent line to the parabola passing through

Explanation / Answer

slope of tangent = 2x x is +ve given let x= a y = 2ax+c pass through (0,-4) ==> c=-4 y = 2ax -4 it touches parabola ==> solve parabola and line and apply for one sol 2ax-4 = x^2 + 4 x^ -2ax +16 = 0 b^2 = 4ac ==> 4a^2 = 16*4 a = +- 4 but a is +ve hence a= 4 point x cordinate is 4

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