Question

Find the y- and x-intercepts and vertex of the function () = 3 2 5 − 2, and then draw a graph.

Answer 1

The y- and x-intercepts and vertex of the function are:

y-intercept = -2.

x-intercept = -2 and 1/3.

vertex = (-0.833, 4.083)

The intercept of a graph is the point where the graph of a line crosses either the x-axis or the y-axis on a coordinate plane. Based on the quadratic function, the y-intercept can be calculated as follows;

`f(x) = 3x^2 +5x -2\\\\f(0) = 3(0)^2 +5(0) -2`

f(0) = 0 + 0 - 2

f(0) = -2.

For the x-intercept, we have;

`f(x) = 3x^2 +5x -2\\\\0 = 3x^2 +5x -2\\\\x = (-b\; \pm \;√(b^2 - 4ac))/(2a)\\\\x = (-5\; \pm \;√(5^2 - 4(3)(-2)))/(2(3))\\\\x = (-5\; \pm \;√(25 +24))/(6)\\\\x = (-5\; \pm \;√(49))/(6)\\\\x = (-5\; \pm \;7)/(6)`

x = -12/6 = -2

x = 2/6 = 1/3.

Based on the graph of this quadratic function
`f(x) = 3x^2 +5x -2`, the vertex is (-0.833, 4.083).

Complete Question;

Find the y- and x-intercepts and vertex of the function
`f(x) = 3x^2 +5x -2`, and then draw a graph.