Match the Quadratic Function y = 2x² + 3 to Its Correct Graph

Video Solution

Solution Steps

00:00 Match the function to the appropriate graph

00:03 Notice the coefficient of X squared is positive, so the function is happy (opens upward)

00:09 We want to find the intersection point with the Y-axis

00:13 Let's substitute X=0 and solve to find the intersection point with the Y-axis

00:19 This is the intersection point with the Y-axis

00:23 According to the function type and intersection point

00:26 We can conclude there are no intersection points with the X-axis

00:29 Let's draw the graph according to the function type and the intersection point we found

00:32 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to match the quadratic function $y = 2x^2 + 3$ with one of the graph choices.

First, identify the characteristics of the parabola:

The standard form of the function is $y = 2x^2 + 3$ , which is already in vertex form for vertical shift.
The parabola opens upwards since the coefficient of $x^2$ is positive ( $a = 2$ ).
The vertex of the parabola is at $(0, 3)$ , not subject to any horizontal shifts. The only transformation from $y = x^2$ is the vertical shift by 3 units up.

Now, assess the graph choices:

Look for a parabola that is centered on the vertical axis (origin along the x-axis) and opens upwards.
Among the provided graphs, the one depicting an upright parabola with vertex at $(0, 3)$ should correspond to our function.

The correct choice is graph 3, as it aligns with our function's characteristics: opening upwards, vertex located at $(0, 3)$ .

Therefore, the solution to the problem is graph 3.