## Related questions with answers

Question

a. Find the vertex and intercepts.

b. Sketch the graph.

c. Confirm your sketch using PLOT CONIC from the accompanying disk, or another suitable graphing program.

Find the vertex and intercepts of the following parabolas, and sketch the graph. Find decimal approximations for any radicals you encounter.

$y=\frac{1}{5} x^2+2 x-\frac{11}{5}$

Solutions

VerifiedSolution A

Solution B

Answered 2 years ago

Step 1

1 of 4**(a)** In general, a parabola is given by the equation

$y = ax^2+bx+c$

The vertex of this parabola is the point $(x_0,y_0)$ given by

$x_0 = -\frac{b}{2a},\,\,\, y_0 = \frac{4ac-b^2}{4a}$

The $x$-intercepts $x_1$ and $x_1$ (if they exist) are given by the formula

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The $y$-intercept is given by $y_1=c$.

Step 1

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