To sketch a graph of a quadratic function with the following conditions:

1. Two real roots (one positive, one negative): This means the graph will intersect the x-axis at two points, one on the positive side and one on the negative side.
2. Opens downwards: The parabola will have a downward shape, meaning the coefficient of the $x^2$ term in the quadratic equation is negative.
3. Y-intercept at (0, 4): The graph crosses the y-axis at the point (0, 4).

Sketch description:

• The graph is a parabola that opens downwards, starting high and curving down to intersect the x-axis at two points: one on the negative side and one on the positive side.
• The vertex is the highest point, located between the two real roots.
• The y-intercept at (0, 4) means the graph crosses the y-axis at 4, so when $x = 0$, $y = 4$.

Would you like me to generate a visual sketch of this graph?

Possible Relative Questions:

1. What does the vertex of a quadratic function represent?
2. How can we determine if a quadratic function has two real roots?
3. What is the general form of a quadratic equation?
4. How does the sign of the leading coefficient affect the direction of the parabola?
5. How can you find the axis of symmetry for a quadratic graph?

Tip:

The y-intercept of a quadratic function is always the constant term in its standard form $y = ax^2 + bx + c$.