The graph of the quadratic function y = 2x^24x1 is pictured below, along with the point P= (1,7) on the parabola and the tangent line through P A line thatis tangent to a parabola does not intersect the parabola at any other point We can use this fact to find the equation of the tangent line (a) If m is the slope of the tangent line, then Graph \(y=2x^{2}4x5\) Solution Because the leading coefficient 2 is positive, note that the parabola opens upward Here c = 5 and the yintercept is (0, 5) To find the xintercepts, set y = 0 \(\begin{array}{l}{y=2 x^{2}4 x5} \\ {0=2 x^{2}4 x5}\end{array}\) In this case, a = 2, b = 4, and c = 5 Use the discriminant to determine the #y=2x^24# To find the vertex, rewrite the function as #y=2x^x4# xcoordinate of the vertex #x=(b)/(2a)=0/(2 xx 2)=0# y coordinate of the vertex At #x=0#;
Graphing Parabolas Using The Vertex Axis Of Symmetry
