Question

1. use factoring to graph the function \\(f(x) = 2x^2 + 5x - 3\\).

drag control points to graph the intercepts and vertex of the quadratic function.

Explanation:

Factor the quadratic function

Using the Factoring Quadratics knowledge point

$$
LATEXBLOCK0
$$

Find the x-intercepts

Set \(f(x) = 0\) to find the intercepts.

$$
LATEXBLOCK1
$$

The x-intercepts are at \((-3, 0)\) and \((0.5, 0)\).

Find the vertex coordinates

Find the vertex using the axis of symmetry.

$$
LATEXBLOCK2
$$

The vertex is at \((-1.25, -6.125)\).

Answer:

To graph the quadratic function \(f(x) = 2x^2 + 5x - 3\), place the control points at:

• x-intercepts: \((-3, 0)\) and \((0.5, 0)\)
• Vertex: \((-1.25, -6.125)\)
• y-intercept: \((0, -3)\)