3 forms of quadratic equations

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the x-coordinate of the vertex of a quadratic equation in standard form?

Back

Use the formula x = -b/(2a).

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If a > 0, it opens upwards; if a < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)² + k, where (h, k) is the vertex.

Front

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

Back

The 'a' value affects the width and direction of the parabola.

Front

How do you convert from standard form to vertex form?

Back

Use completing the square method.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the number of real roots: positive (two roots), zero (one root), negative (no real roots).

Tags

CCSS.HSA-REI.B.4B