First Rewrite the Quadratic Function in Standard Form by Completing $f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$

question 36

Multiple Choice

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
- $f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$ Give your answers in exact form.

• A) \(x\)-intercepts: \(\frac { - 10 - \sqrt { 13 } } { 3 }\) and \(\frac { - 10 + \sqrt { 13 } } { 3 } ; y\)-intercept: 0
• B) x-intercepts: \(\frac { - 5 - \sqrt { 13 } } { 6 }\) and \(\frac { - 5 + \sqrt { 13 } } { 6 } ; y\)-intercept: 4
• C) \(x\)-intercepts: \(\frac { - 5 - \sqrt { 13 } } { 3 }\) and \(\frac { - 5 - \sqrt { 13 } } { 3 } ; y\)-intercept: 4
• D) \(x\)-intercepts: \(\frac { - 5 - \sqrt { 37 } } { 3 }\) and \(\frac { - 5 + \sqrt { 37 } } { 3 } ; y\)-intercept: 0

---

Definitions:

Posterior Cruciate Ligament

A ligament in the knee that connects the femur to the tibia, stabilizing the knee joint.

Fibular Collateral Ligament

A ligament on the lateral side of the knee that connects the femur to the fibula, stabilizing the knee joint.

Hyperextension

A movement that increases the angle between two body parts beyond the normal range of motion, often referring to joints.

Dorsiflexion

The movement that brings the top of the foot toward the shin, decreasing the angle between them.