Math 3 wk 1

Front

What is the equation of a parabola given its vertex and a point it passes through?

Back

To find the equation of a parabola given its vertex (h, k) and a point (x, y), use the vertex form: y = a(x - h)² + k. Substitute the vertex and the point to solve for 'a'.

Front

What is the process of rounding numbers?

Back

Rounding is the process of adjusting the digits of a number to make it simpler while keeping its value close to what it was. For example, rounding 3.25 to the nearest tenth gives 3.3.

Front

How do you identify the function from its graph?

Back

To identify a function from its graph, look for key features such as the direction of the parabola (upward or downward), vertex, and intercepts. Compare these features with the standard forms of quadratic functions.

Front

What is the positive solution of the equation x² = 2x + 35?

Back

To solve x² = 2x + 35, rearrange to x² - 2x - 35 = 0. Factor or use the quadratic formula to find the positive solution, which is x = 7.

Front

How do you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in the form y = ax² + bx + c, the vertex can be found using the formula: x = -b/(2a). Substitute this x-value back into the equation to find the y-coordinate.

Front

What is the vertex of the parabola y = x² + 8x + 5?

Back

The vertex of the parabola y = x² + 8x + 5 is (-4, -11), found using the vertex formula.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' value in a quadratic function indicate?

Back

In a quadratic function y = ax² + bx + c, the 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form y = a(x - h)² + k, complete the square.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry of a parabola is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).