Question

Liesa wants to graph k(x) = 2(x + 3)^2 − 5. She thinks that the vertex of the parabola should be (6, -5), because 2*3=6, and there's a (-5) at the end. She plots that vertex, and then graphs a parent function upward from there. She ends up with the graph shown. Explain whether you agree or disagree with Liesa's work, and what you would have done differently, if you disagree. Answer specifically about the vertex, y-intercept, and the shape and orientation of the parabola.

Answer 1

I disagree with Liesa's work. The correct vertex of the parabola is (-3, -5), and the y-intercept is (0, 13). The parabola opens upwards with a narrow shape.

Step-by-step explanation:

I disagree with Liesa's work. The correct vertex of the parabola represented by the equation k(x) = 2(x + 3)^2 - 5 is (-3, -5), not (6, -5). The x-coordinate of the vertex is found by setting the expression inside the parentheses equal to 0 and solving for x. In this case, x + 3 = 0, so x = -3. Substituting this value into the equation, we find that k(-3) = 2(-3 + 3)^2 - 5 = 2(0)^2 - 5 = -5. Therefore, the correct vertex is (-3, -5).

Additionally, the y-intercept of the parabola can be found by setting x = 0 in the equation. Plugging in x = 0, we get k(0) = 2(0 + 3)^2 - 5 = 2(3)^2 - 5 = 18 - 5 = 13. So the y-intercept is (0, 13).

The shape and orientation of the parabola can be determined by the coefficient in front of the squared term, which is 2 in this case. Since the coefficient is positive, the parabola opens upwards. The larger the coefficient, the narrower the parabola.