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

Video Solution

Solution Steps

00:06 Let's match the function to the right graph.

00:09 Because the coefficient of X squared is positive, the graph opens upward. It's like a happy face.

00:16 Next, let's find where the graph crosses the Y-axis.

00:20 Substitute X equals zero to see where it intersects the Y-axis.

00:26 This point is where our graph crosses the Y-axis.

00:29 Based on the function type and the Y-intercept,

00:33 we conclude there are no points where it intersects the X-axis.

00:38 Now, let's draw the graph using the function type and our intersection point.

00:43 And that's how we solve this problem!

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.