Let's Practice
Are you ready to take this lesson's quiz? The questions below will help you find out. Make sure you understand why each correct answer is correct--if you don't, review that part of the lesson.
Which quadratic equation is written in standard form?
- \( 2x^{2} + 15x = 8 \)
- \( 2x^{2} - 8 = - 15x \)
- \( 2x^{2} + 15x - 8 = 0 \)
- \( 2x^{2} + 15x - 8 = 10 \)
The standard form of a quadratic equation is \( ax^{2} + bx + c = 0 \).
The standard form of a quadratic equation is \( ax^{2} + bx + c = 0 \).
The standard form of a quadratic equation is \( ax^{2} + bx + c = 0 \).
The standard form of a quadratic equation is \( ax^{2} + bx + c = 0 \).
Which is the best definition of discriminant?
- An equation in which the largest exponent is 2.
- The value of the expression under the radical in the quadratic formula.
- A number in the form \( a + bi \).
- The product of two identical binomials.
This is the definition of a quadratic equation.
The discriminant is equal to \( \sqrt{b^{2} - 4ac} \).
This is the definition of a complex number.
This is the definition of a perfect square trinomial.
Which are the solutions of \( x^{2} + 8x + 5 = 0 \)?
- \( ( - 7.32,0) \) and \( ( - 0.68,\ 0) \)
- \( x = - 7.32,\ x = - 0.68 \)
- \( ( - 4, - 11) \)
- \( x = 0,\ x = - 4 \)
Solutions to quadratic equations are expressed as ordered pairs.
These are the roots of the equation.
This is the location of the vertex.
Solutions to quadratic equations are expressed as ordered pairs.
Which is the value of the discriminant of \( x^{2} - 3x = 18 \)?
- \( d = \sqrt{81} \)
- \( d = \sqrt{75} \)
- \( d = \sqrt{- 63} \)
- \( d = \sqrt{- 9} \)
The discriminant is equal to \( \sqrt{b^{2} - 4ac} \).
The discriminant is equal to \( \sqrt{b^{2} - 4ac} \).
The discriminant is equal to \( \sqrt{b^{2} - 4ac} \).
The discriminant is equal to \( \sqrt{b^{2} - 4ac} \).
Is it possible for a quadratic equation to have one real number solution and one complex number solution? Explain.
- No. For a quadratic equation to have one real and one complex number solution, the discriminant would need to be both zero and positive at the same time.
- No. For a quadratic equation to have one real and one complex number solution, the discriminant would need to be both positive and negative at the same time.
- Yes. A quadratic equation can have a real number and a complex number solution when it is written in standard form.
- Yes. A quadratic equation can have a real number and a complex number solution when the value of the discriminant is less than \( - \)15.
A real number solution occurs when the discriminant is positive. A complex number solution occurs when the discriminant is negative.
A real number solution occurs when the discriminant is positive. A complex number solution occurs when the discriminant is negative.
A real number solution occurs when the discriminant is positive. A complex number solution occurs when the discriminant is negative.
A real number solution occurs when the discriminant is positive. A complex number solution occurs when the discriminant is negative.
How many solutions will the quadratic equation \( 2x^{2} - 6x + 9 = 0 \) have?
- This equation has no solution.
- Two real number solutions.
- One real number solution.
- Two complex number solutions.
A quadratic equation always has at least one solution.
A quadratic equation has two real number solutions when the value of the discriminant is greater than 0.
A quadratic equation has one real number solution when the value of the discriminant is exactly 0.
A quadratic equation has two complex number solutions when the value of the discriminant is less than 0.
If the value of the discriminant is less than 0, what is true about the graph of the quadratic equation?
- The quadratic equation cannot be graphed.
- The graph of the quadratic equation will cross the x-axis twice.
- The graph of the quadratic equation will touch the x-axis in one place.
- The graph of the quadratic equation will not touch the x-axis.
All quadratic equations can be graphed.
This occurs when the discriminant is greater than 0.
This occurs when the discriminant is exactly than 0.
This occurs when the discriminant is less than 0.
Which is the correct substitution of \( 3x = - 5x^{2} + 12 \) into the quadratic formula?
- \( x = \frac{(3) \pm \sqrt{{(3)}^{2} - 4(5)(12)}}{2(5)} \)
- \( x = \frac{(3) \pm \sqrt{{(3)}^{2} - 4( - 5)(12)}}{2( - 5)} \)
- \( x = \frac{- (3) \pm \sqrt{{(3)}^{2} - 4(5)( - 12)}}{2(5)} \)
- \( x = \frac{- (3) \pm \sqrt{{( - 3)}^{2} - 4( - 5)( - 12)}}{2( - 5)} \)
Write the quadratic equation in standard form, identify the values of a, b, and c. Then substitute those values into the quadratic formula. The quadratic formula is \( x = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a} \).
Write the quadratic equation in standard form, identify the values of a, b, and c. Then substitute those values into the quadratic formula. The quadratic formula is \( x = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a} \).
Write the quadratic equation in standard form, identify the values of a, b, and c. Then substitute those values into the quadratic formula. The quadratic formula is \( x = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a} \).
Write the quadratic equation in standard form, identify the values of a, b, and c. Then substitute those values into the quadratic formula. The quadratic formula is \( x = \frac{- b \pm \sqrt{b^{2} - 4ac}}{2a} \).
Summary
Questions answered correctly:
Questions answered incorrectly:
