Question

what is an equation of a parabola with the y - intercept of (0,6)? 1. $y = 2x^2 + 3x - 6$ 2. $y = 2x^2 + 4x + 10$ 3. $y = - 2x^2 - 8x + 6$ 4. $y = x^2 + x - 6$

Explanation:

Step1: Recall y - intercept rule

To find the y - intercept of a parabola given by the equation \(y = ax^{2}+bx + c\), we set \(x = 0\). When \(x = 0\), the equation simplifies to \(y=c\). So we need to check which of the given equations has \(c = 6\) (since the y - intercept is \((0,6)\)).

Step2: Check each equation

• For \(y=2x^{2}+3x - 6\): When \(x = 0\), \(y=-6\). So this is not the correct equation.
• For \(y = 2x^{2}+4x + 10\): When \(x = 0\), \(y = 10\). So this is not the correct equation.
• For \(y=-2x^{2}-8x + 6\): When \(x = 0\), \(y=6\). This satisfies the y - intercept condition.
• For \(y=x^{2}+x - 6\): When \(x = 0\), \(y=-6\). So this is not the correct equation.

Answer:

\(y=-2x^{2}-8x + 6\) (the third option, with the orange background)