Solve Quadratics by Square Roots

Front

What causes the graph of y = x² to open downward?

Back

Multiplying the x² by a negative number.

Front

How do you solve the equation -9p² = -576 for p?

Back

Divide both sides by -9 to get p² = 64, then take the square root to find p = 8 and p = -8.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola.

Front

How do you find the y-intercept of the function y = x² + 4x - 7?

Back

Set x = 0 and solve for y, which gives the point (0, -7).

Front

How do you solve the equation (h - 2)² = 9 for h?

Back

Take the square root of both sides to get h - 2 = 3 or h - 2 = -3, leading to h = 5 or h = -1.

Front

What is the vertex of a parabola in the form y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting back to find the y-coordinate.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

If the coefficient 'a' in y = ax² + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the formula for the vertex of a parabola given in vertex form y = a(x - h)² + k?

Back

The vertex is the point (h, k).