Match each statement with its corresponding graph in choices A...

Question

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx²)

Four graphs labeled A to D showing different curves of y versus x, illustrating variations of y = kx² with k > 0.

Accepted Answer

Welcome back. I am so glad you're here. We are asked to draw the graph for the following variation problem. We're using the symbol K for the constant of variation. And here is our problem and we're told that Y varies directly as the square of K, right? So let's break that down into an equation. We're told why. So we're given Y equals when we're told why now it varies directly. All right, that's direct variation. We recall from previous lessons that varying directly means we are going to be multiplying the constant term K by what remains. So we're going to have Y equals K multiplied by. And now what's left the square of X? OK. That's X squared. So K X squared, we have Y equals K X squared where K is our constant, we know that K is going to be greater than zero. And that's important for our graph. If we draw a rough sketch of a coordinate plane, we have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle X squared, just X squared by itself or Y equals X squared. We know that that is going to be a Parabola and the number directly in front of our X squared for a parabola tells us whether this is going to be facing upward or downward. Well, K is greater than zero. So because K is greater than zero, it's usually like where our A goes, our A is greater than zero, that tells us that this opens upward. Now, the only shift that's happening here is the K being multiplied by the X squared. We know it's going to be greater than zero, it's going to open upward. So there could be some vertical stretching or shrinking going on here. So we don't know the exact scale of what's happening to our X squared, but we know it'll be a parabola opening upward and there, we've got our graph well done. We'll catch you on the next one.

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx²)

Key Concepts

Direct Variation

Quadratic Functions and Their Graphs

Effect of the Constant k on the Graph

Watch next

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx2)

Key Concepts

Direct Variation

Quadratic Functions and Their Graphs

Effect of the Constant k on the Graph

Watch next

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx²)