Math 2 Unit 5 end of lesson 5 practice

Front

What is the leading coefficient in the quadratic equation y = x^2 + 5x + 7?

Back

The leading coefficient is 1.

Front

What is the value of the discriminant in the quadratic equation y = x^2 + 5x + 7?

Back

The discriminant is 25 - 4(1)(7) = 25 - 28 = -3.

Front

How do you calculate the discriminant of a quadratic equation?

Back

The discriminant is calculated using the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √D) / (2a), where D is the discriminant.

Front

Solve using the quadratic formula: 2x^2 + 7x - 15 = 0

Back

The solutions are x = -5 and x = 1.5.

Front

What is the value of the discriminant for the equation 2x^2 + 7x - 15 = 0?

Back

The discriminant is 7^2 - 4(2)(-15) = 49 + 120 = 169.

Front

What is the leading coefficient in the polynomial y = 3x^3 + 8x - 1?

Back

The leading coefficient is 3.

Front

Use the quadratic formula to find the solutions for y = 3x^3 + 8x - 1.

Back

The solutions are approximately x = 0.1167 and x = -2.7833.

Front

What does the leading coefficient tell us about the graph of a quadratic function?

Back

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