Graphing Parabolas standard form

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the coefficient 'a' indicate in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the x-coordinate of the vertex of a parabola given the equation y = ax² + bx + c?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) are the x-values where the graph of the function intersects the x-axis (y=0).

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the direction a parabola opens from its equation?

Back

Look at the coefficient 'a': if 'a' > 0, it opens up; if 'a' < 0, it opens down.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of the parabola, depending on its direction.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x=0.

Tags

CCSS.HSF-IF.C.7A

Front

How do you graph a quadratic function in standard form?

Back

1. Identify the vertex using x = -b/(2a). 2. Calculate the y-coordinate of the vertex. 3. Find the y-intercept. 4. Plot points and draw the parabola.

Tags

CCSS.HSF-IF.C.7A

Front

What is the difference between standard form and vertex form of a quadratic equation?

Back

Standard form is y = ax² + bx + c; vertex form is y = a(x - h)² + k, where (h, k) is the vertex.