Graphing Quadratic Equations

Front

What are the coordinates of the y-intercept of a quadratic equation?

Back

(0, c) where c is the constant term in the equation y = ax^2 + bx + c.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side.

Front

What does it mean if a quadratic has a maximum vertex?

Back

The parabola opens downwards and the vertex is the highest point on the graph.

Front

Identify the values of a, b, and c in the quadratic equation 9x² - 14x + 5.

Back

a = 9, b = -14, c = 5.

Front

What is the general form of a quadratic equation?

Back

y = ax² + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.

Front

What does the 'a' value in a quadratic equation determine?

Back

The direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the y-intercept of the function y = x² - 4x?

Back

(0, 0) because when x = 0, y = 0² - 4(0) = 0.

Front

How can you determine if a quadratic equation has real roots?

Back

By calculating the discriminant: D = b² - 4ac. If D > 0, there are two real roots; if D = 0, one real root; if D < 0, no real roots.