Question

question 12 (5 points)
what are the features of the quadratic function graphed in the figure?

a) vertex = \\((-4,3)\\), y-intercept = \\((5,0)\\), x-intercepts = \\((0,1)\\) and \\((0,5)\\), axis of symmetry is \\(x = -4\\)

b) vertex = \\((3,-4)\\), y-intercepts = \\((-1,0)\\) and \\((-5,0)\\), x-intercept = \\((0,5)\\), axis of symmetry is \\(x = 3\\)

c) vertex = \\((-3,4)\\), y-intercept = \\((0,-5)\\), x-intercepts = \\((-5,0)\\) and \\((-1,0)\\), axis of symmetry is \\(x = -3\\)

d) vertex = \\((-3,4)\\), y-intercept = \\((0,-5)\\), x-intercepts = \\((1,0)\\) and \\((5,0)\\), axis of symmetry is \\(x = -3\\)

Explanation:

Identify the vertex of the parabola

Using the Parabola Vertex Form knowledge point

$$ \text{Vertex } (h, k) = (-3, 4) $$

Determine the axis of symmetry

The axis of symmetry is the vertical line passing through the x-coordinate of the vertex.

$$ x = -3 $$

Find the y-intercept

Using the Quadratic y-intercept knowledge point

$$ (0, -5) $$

Identify the x-intercepts

The graph crosses the x-axis at two points.

$$ (-5, 0) \quad \text{and} \quad (-1, 0) $$

Match with the correct option

We compare our identified features with the given choices:

• Option A: Vertex is incorrect.
• Option B: Vertex is incorrect.
• Option C: Vertex \( = (-3,4) \), y-intercept \( = (0,-5) \), x-intercepts \( = (-5,0) \) and \( (-1,0) \), axis of symmetry is \( x = -3 \). This matches perfectly.
• Option D: x-intercepts are incorrect.

Answer:

• A) Vertex = (-4,3), y-intercept = (5,0), x-intercepts = (0,1) and (0,5), axis of symmetry is x = -4
• B) Vertex = (3,-4), y-intercepts = (-1,0) and (-5,0), x-intercept = (0,5), axis of symmetry is x = 3
• C) Vertex = (-3,4), y-intercept = (0,-5), x-intercepts = (-5,0) and (-1,0), axis of symmetry is x = -3 (Correct answer)
• D) Vertex = (-3,4), y-intercept = (0,-5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = -3