Question

question
using the graph, determine the coordinates of the x-intercepts of the parabola.
answer attempt 2 out of 2
answer type: one equation
one equation:

Explanation:

Step1: Identify x-intercepts

The x-intercepts are points where the parabola crosses the x - axis (where \(y = 0\)). From the graph, the parabola crosses the x - axis at \(x=-6\) and \(x = - 4\).

Step2: Write the equation

If the x - intercepts of a quadratic function (parabola) are \(x=a\) and \(x = b\), the factored form of the quadratic equation is \(y=(x - a)(x - b)\). Here, \(a=-6\) and \(b = - 4\), so \(y=(x+6)(x + 4)\). We can also expand it: \(y=x^{2}+10x + 24\) (or keep it in factored form). But since the question says "one equation" (probably the equation of the parabola with the x - intercepts), we can write the factored form or the standard form. The x - intercepts are at \((-6,0)\) and \((-4,0)\), and the equation of the parabola can be written as \(y=(x + 6)(x+4)\) (or expanded). But if we consider the x - intercepts as points, but the question says "answer type: one equation", so we need to write the equation of the parabola. Alternatively, if we just need to state the x - intercepts as coordinates, but the answer type is one equation. Wait, maybe the question is to write the equation of the parabola with x - intercepts at \(x=-6\) and \(x=-4\). So the equation is \(y=(x + 6)(x + 4)\) or \(y=x^{2}+10x + 24\). But let's check the graph. The vertex is at \(x=-5\) (mid - point of \(-6\) and \(-4\)), and the parabola opens upwards. So the equation is \(y=(x + 6)(x + 4)\).

Answer:

\(y=(x + 6)(x + 4)\) (or \(y=x^{2}+10x + 24\))