(a) Consider the parabola which is the graph of f(x) = 2x + 3x + 8....

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(a) Consider the parabola which is the graph of f(x) = 2x² + 3x + 8. The tangent line to this parabola at the point (a, f(a)) will have what y-intercept? (Your answer should be in terms of a.) (b) How many tangent lines to this parabola pass through the origin? (What does passing through the origin have to do with y-intercept?) (c) How many tangent lines to this parabola pass through the point (0,20)? (d) Draw a picture illustrating the previous two parts. (a) Consider the parabola which is the graph of f(x) = 2x² + 3x + 8. The tangent line to this parabola at the point (a, f(a)) will have what y-intercept? (Your answer should be in terms of a.) (b) How many tangent lines to this parabola pass through the origin? (What does passing through the origin have to do with y-intercept?) (c) How many tangent lines to this parabola pass through the point (0,20)? (d) Draw a picture illustrating the previous two parts.