How do you use the important points to sketch the graph of #5x^2 - 3x + 2#?

Question

Julia Adams · Accepted Answer

Find the points that are easy to find.

For #5x^2−3x+2 #, you should take the easiest point possible: the point where x=0. #5(0^2)-3(0)+2# is equal to 0-0+2=2. Thus we know that one point is #(0, 2)#. Then we could plug in a small random number such as 2. #5(2^2)-3(2)+2# #5(4)-6+2# #20-6+2# That will equal 16. So we know another point on our graph is (2, 16). But since this is a parabola that faces up, we need another point. #5(-1^2)-3(-1)+2# #5(1)+3+2# Hence we can infer another point is (-1, 10) graph{5x^2-3x+2 [-40, 40, -20, 20]} With the 3 points we have, we can draw the graph with artistic flair now.

Eli Assouline · Answer

undefined To sketch the graph of $5x^2 - 3x + 2$, you would first identify the vertex, which is the point where the parabola reaches its minimum or maximum value. The x-coordinate of the vertex is given by $-\frac{b}{2a}$, where $a = 5$ and $b = -3$ from the quadratic equation $ax^2 + bx + c$. Then, substitute this x-coordinate into the equation to find the y-coordinate of the vertex. Additionally, you can find the y-intercept by substituting $x = 0$ into the equation. Plot these points on the coordinate plane and use the symmetry of the parabola to sketch the rest of the curve.