Question

solve the equation by graphing the related function.
$x^2 + 3x + 4 = 0$
graph the related function. choose the correct answer below.
oa
ob
oc
od

Explanation:

Step1: Define related function

The related function is $y = x^2 + 3x + 4$.

Step2: Find vertex of parabola

Vertex x-coordinate: $x = -\frac{b}{2a} = -\frac{3}{2(1)} = -1.5$
Substitute $x=-1.5$ into the function:
$y = (-1.5)^2 + 3(-1.5) + 4 = 2.25 - 4.5 + 4 = 1.75$
Vertex is $(-1.5, 1.75)$.

Step3: Determine parabola direction

Since $a=1>0$, parabola opens upward.

Step4: Check x-intercepts

Calculate discriminant: $\Delta = b^2 - 4ac = 3^2 - 4(1)(4) = 9 - 16 = -7 < 0$
No real x-intercepts, so the parabola never crosses the x-axis.

Answer:

A. <Graph of upward-opening parabola with vertex in the second quadrant, no x-intercepts>