Graph each quadratic equation by finding and plotting ordered pair solutions.
$y=2x^2+5$

• A.
• B.
• C.
• D.

Answer: (D)

Verified step by step guidance

1. Identify the quadratic equation given: \(y = 2x^2 + 5\). This is a parabola opening upwards because the coefficient of \(x^2\) is positive.
2. Choose several values for \(x\) to find corresponding \(y\) values. For example, use \(x = -2, -1, 0, 1, 2\).
3. Calculate \(y\) for each chosen \(x\) using the equation \(y = 2x^2 + 5\). For instance, when \(x = -2\), calculate \(y = 2(-2)^2 + 5\).
4. Plot each ordered pair \((x, y)\) on the coordinate grid. For example, plot the point \((-2, y)\) where \(y\) is the value calculated in the previous step.
5. Connect the plotted points smoothly to form the parabola, ensuring it opens upwards and is symmetric about the \(y\)-axis.