Question

The equation of a quadratic is =2^2+3−2and after you factorizing 2^2+3−2=0you got x = -2 and x = 1/2 and the curve crosses the y-axis at (0,-2)Using the information above, sketch the graph of =2^2+3−2

Answer 1

Given the next quadratic function:

`y=2x^2+3x-2`

to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:

`x_V=(-b)/(2a)`

where a and b are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:

`\begin{gathered} x_V=(-3)/(2\cdot2) \\ x_V=-(3)/(4)=-0.75 \end{gathered}`

The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:

`\begin{gathered} y_V=2x^2_V+3x_V-2 \\ y_V=2\cdot(-(3)/(4))^2+3\cdot(-(3)/(4))-2 \\ y_V=2\cdot(9)/(16)+3\cdot(-(3)/(4))-2 \\ y_V=(9)/(8)-(9)/(4)-2 \\ y_V=-(25)/(8)=-3.125 \end{gathered}`

The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get: