How do you draw the graph of y=3x2−7?

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stamptsk · Accepted Answer

Step 1  Note that y=3x2−7 is parabola (which opens upward) so we will need to calculate a few sample points and then draw a parabolic curve through those points.  For example you might calculate f(x) for all integer values in the range [−−4, +4] (note symmetry about the Y-axis reduces the number of actual calculations).  (−4, 41) and (+4, 41)  (−3, 20) and (+3, 20)  (−2, 5) and (+2, 5)  (−1, −4) and (+1, −4)  (0, −7)  Mark these point on some graph paper and joint them in a smooth curve that should look something like:  Graph: {3x2−7[−9.71, 10.29, −7.16, 2.84]}

Howard Gallagher · Accepted Answer

Step 1  Given:  y=3x2−7 is a quadratic equation in standard form:  y=ax2+bx+c  where:  a=3, b=0, c=−7  To graph a parabola you need to determine the following points:  axis of symmetry, vertex, y-intercept (if applicable), x-intercepts (if applicable), and additional points if needed.  Axis of symmetry: vertical line that divides the parabola into two equal halves  Vertex: the maximum or minimum point of the parabola.  The formula for determining the axis of symmetry, which is also the x-coordinate of the vertex is:  x=−b2a  x=02×3  x=0  To determine the y-coordinate by substituting 0 for x and solving for y.  y=3(0)2−7  y=−7  The vertex is (0, −7)  Y-intercept: value of y when x=0  In this particular case, the y-intercept is the same as the vertex, (0, −7)  X-intercepts: values of x when y=0  0=3x−7  Add 7 to both sides  7=3x2  Divide both sides by 3.  73=x2  ±73=x  x=−73, 73  The x-intercepts are (−73, 0) and (73, 0)  The approximate x-intercepts are (−1.528, 0) and (1.528, 0)  Additional points: Choose values for x and solve for y.  Plot the points and sketch a parabola through them. Do not connect the dots.  Graph: {y=3x2−7[−9.88, 10.12, −7.88, 2.12]}

How do you draw the graph of y=3x^{2}-7?

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