Question

1. write an expression for \\(\sqrt{175}\\) without a perfect square factor in the radicand.

1. adam graphs a quadratic function. the vertex of the parabola he graphs is located at (-5, 0). which of the following is the axis of symmetry?

a \\(x = -5\\)
b \\(x = 0\\)
c \\(x = 5\\)
d \\(x = y\\)

Explanation:

Question 3

Step1: Factor 175

Find the largest perfect square factor of 175. \(175 = 25\times7\), where 25 is a perfect square (\(5^2\)).

Step2: Simplify the square root

Use the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0, b\geq0\)). So \(\sqrt{175}=\sqrt{25\times7}=\sqrt{25}\times\sqrt{7}=5\sqrt{7}\).

For a quadratic function (parabola), the axis of symmetry is a vertical line that passes through the vertex. The vertex is at \((-5, 0)\), so the axis of symmetry has the equation \(x = -5\) (since the x - coordinate of the vertex gives the equation of the vertical axis of symmetry).

Answer:

\(5\sqrt{7}\)

Question 4