Question

graph the quadratic.
a) d
c) b

1. y = 3x² + 12x + 13 (with four graphs labeled a, b, c, d)

Explanation:

Step1: Analyze the quadratic function

The quadratic function is \( y = 3x^2 + 12x + 13 \). First, we can find the vertex of the parabola. The x - coordinate of the vertex of a quadratic function \( y=ax^{2}+bx + c \) is given by \( x=-\frac{b}{2a} \). For \( a = 3 \) and \( b=12 \), we have \( x=-\frac{12}{2\times3}=- 2 \).

Step2: Find the y - coordinate of the vertex

Substitute \( x = - 2 \) into the function: \( y=3\times(-2)^{2}+12\times(-2)+13=3\times4-24 + 13=12-24 + 13=1 \). So the vertex is at \( (-2,1) \).

Step3: Analyze the direction of the parabola

Since \( a = 3>0 \), the parabola opens upwards.

Step4: Match with the graphs

We need to find the graph with vertex at \( (-2,1) \) and opening upwards. Looking at the given graphs, we check the vertex and the direction. The graph that has its vertex at \( (-2,1) \) and opens upwards is the correct one. From the options, we can see that the graph corresponding to the correct vertex and direction is the one that we can identify (assuming the graphs are labeled such that one of them has vertex at (-2,1) and opens up).

Answer:

The graph that represents \( y = 3x^2+12x + 13 \) (with vertex at \((-2,1)\) and opening upwards)