Question

I am sketching parabolas and my book is telling me that I need only two points. But I don't know how I am meant to sketch the parabola accurately with only two points. Are parabolas just supposed to be drawn roughly or do we have to find all the points and then sketch it?

Answer 1

In order to sketch a parabola, one will typically use the y-intercept, the x-intercepts, and the vertex.

Explanation:

In order to sketch a parabola, one will typically use the given equation in standard form,
`y = ax^2 + bx + c`, and:

• The y-intercept – the point where the parabola crosses the vertical axis – by substituting 0 for all x values in the given equation and solving for y.
• The x-intercepts – the points where the parabola crosses the horizontal axis – by setting the given equation equal to 0 (i.e., y = 0) and finding the factors (or roots).
• The vertex – the point of symmetry where the parabola changes direction and curves up or down – by using
  `x=(-b)/(2a)` to find the x-coordinate then plugging that value into the given equation to find the y-coordinate.