Question

use a graphing utility to find or to approximate the x - intercept(s) of the graph of the function.
y = 5x²+17x - 12
graph the function y = 5x²+17x - 12. choose the correct graph below
graphs are shown in -10,10 by -50,50 viewing rectangles with xscl = 1 and yscl = 5.

Explanation:

Step1: Determine the parabola's direction

For the quadratic function \(y = ax^{2}+bx + c\), here \(a = 5\gt0\). So the parabola opens upwards.

Step2: Analyze each option

• Option B and C: Parabolas open downwards (\(a\lt0\) for them, which is not the case for \(y = 5x^{2}+17x - 12\)).
• Option D: The vertex is on the \(y\) - axis. For \(y=5x^{2}+17x - 12\), the \(x\) - coordinate of the vertex is \(x=-\frac{b}{2a}=-\frac{17}{10}=-1.7

eq0\).

• Option A: Parabola opens upwards (since \(a = 5\gt0\)) and has non - zero \(x\) - coordinate of the vertex.

Answer:

A.